(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 67767, 2032]*) (*NotebookOutlinePosition[ 95922, 3052]*) (* CellTagsIndexPosition[ 95776, 3043]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Handbook of Mathematical \n Functions", FontWeight->"Bold"], " -- excerpts" }], "Title", TextAlignment->Center, FontSize->33, FontSlant->"Italic", Background->RGBColor[0, 1, 1]], Cell["(Abramowitz & Stegun)", "Subtitle", TextAlignment->Center, FontSlant->"Italic", Background->RGBColor[1, 1, 0]], Cell[TextData[{ "Chapter 1: Mathematical Constants\nChapter 3: Elementary Analytical \ Methods\nChapter 4: Elementary Transcendental Functions\nChapter 5: \ Exponential Integral and Related Functions\nChapter 6: ", ButtonBox["Gamma", ButtonData:>"Gamma", ButtonStyle->"Hyperlink"], " Function and Related Functions\nChapter 7: Error Function and Fresnel \ Integrals\nChapter 9: ", ButtonBox["Bessel", ButtonData:>"bessel", ButtonStyle->"Hyperlink"], " Functions of Integer Order" }], "Text", FontSize->24], Cell[CellGroupData[{ Cell["Chapter 1: Mathematical Constants", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(Table[{Prime[n], N[Sqrt[Prime[n]], 20]}, {n, 30}] // TableForm\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"2", "1.4142135623730950488016887242097`20"}, {"3", "1.7320508075688772935274463415059`20"}, {"5", "2.2360679774997896964091736687313`20"}, {"7", "2.6457513110645905905016157536393`20"}, {"11", "3.3166247903553998491149327366707`20"}, {"13", "3.60555127546398929311922126747`20"}, {"17", "4.123105625617660549821409855974`20"}, {"19", "4.35889894354067355223698198386`20"}, {"23", "4.795831523312719541597438064163`20"}, {"29", "5.38516480713450403125071049154`20"}, {"31", "5.567764362830021922119471298919`20"}, {"37", "6.082762530298219688999684245202`20"}, {"41", "6.403124237432848686488217674622`20"}, {"43", "6.557438524302000652344109997636`20"}, {"47", "6.855654600401044124935871449085`20"}, {"53", "7.280109889280518271097302491527`20"}, {"59", "7.681145747868608175769687021731`20"}, {"61", "7.810249675906654394129722735759`20"}, {"67", "8.185352771872449969953703724734`20"}, {"71", "8.426149773176358630634139906203`20"}, {"73", "8.54400374531753116787164832624`20"}, {"79", "8.888194417315588850091441675409`20"}, {"83", "9.110433579144298881945626104689`20"}, {"89", "9.433981132056603811320660377623`20"}, {"97", "9.848857801796104721746211414918`20"}, {"101", "10.04987562112089027021926491276`20"}, {"103", "10.148891565092219468648520118936`20"}, {"107", "10.344080432788600469738599442627`20"}, {"109", "10.440306508910550179757754022548`20"}, {"113", "10.630145812734649407999121914929`20"} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], (TableForm[ #]&)]], "Output", TextAlignment->Center, CellTags->"primes"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Chapter 3: Elementary Analytical Methods", "Section"], Cell[BoxData[ RowBox[{\(\((a + b)\)\^n\), " ", "=", " ", RowBox[{\(a\^n\), "+", " ", RowBox[{ RowBox[{"(", GridBox[{ {"n"}, {"1"} }], ")"}], \(a\^\(n - 1\)\), "b"}], " ", "+", " ", RowBox[{ RowBox[{"(", GridBox[{ {"n"}, {"2"} }], ")"}], \(a\^\(n - 2\)\), \(b\^2\)}], " ", "+", " ", RowBox[{ RowBox[{"(", GridBox[{ {"n"}, {"3"} }], ")"}], \(a\^\(n - 3\)\), \(b\^3\)}], " ", "+", " ", "\[CenterEllipsis]", " ", "+", " ", \(b\^n\)}]}]], "Output", CellFrame->{{0, 0}, {0.5, 0}}, FontFamily->"Times", FontSize->24, FontWeight->"Plain", FontSlant->"Italic", Background->RGBColor[1, 1, 0]], Cell[CellGroupData[{ Cell[BoxData[ \(Abs[a\_1]\ - \ Abs[a\_2]\ \ \[LessEqual] \ Abs[a\_1 + a\_2]\ \[LessEqual] \ Abs[a\_1] + Abs[a\_2]\ // \ TraditionalForm\)], "Input"], Cell[BoxData[ \(TraditionalForm \`\[LeftBracketingBar]a\_1\[RightBracketingBar] - \[LeftBracketingBar]a\_2\[RightBracketingBar] \[LessEqual] \[LeftBracketingBar]a\_1 + a\_2\[RightBracketingBar] \[LessEqual] \[LeftBracketingBar]a\_1\[RightBracketingBar] + \[LeftBracketingBar]a\_2\[RightBracketingBar]\)], "Output", FontSize->24, Background->RGBColor[1, 1, 0]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Chapter 4: Elementary Transcendental Functions", "Section"], Cell[BoxData[ \(TraditionalForm \`ln(\(z + 1\)\/\(z - 1\)) == 2\ \((1\/z + 1\/\(3\ z\^3\) + 1\/\(5\ z\^5\) + \[CenterEllipsis])\)\)], "Input", FontSize->24, Background->RGBColor[0, 1, 1]], Cell[BoxData[ \(TraditionalForm \`\[Integral]ln\ z\ \[DifferentialD]z\ \ \ = \ \ \ z\ \(ln(z)\) - z\)], "Input", FontSize->24, Background->RGBColor[0, 1, 0]] }, Open ]], Cell[CellGroupData[{ Cell["Chapter 5: Exponential Integral and Related Functions", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(Integrate[Exp[t]/t, \ {t, \(-Infinity\), \ x}]\ // \n \t\t\t\t\t\t\t\t\t\t\t\t\ TraditionalForm\)], "Input", FontSize->16], Cell[BoxData[ FormBox[ RowBox[{"If", "[", RowBox[{\(x < 0\), ",", \(-\(\[CapitalGamma](0, \(-x\))\)\), ",", RowBox[{ SubsuperscriptBox["\[Integral]", InterpretationBox[\(-\[Infinity]\), DirectedInfinity[ -1]], "x"], \(\(\[ExponentialE]\^t\/t\)\[DifferentialD]t\)}]}], "]"}], TraditionalForm]], "Output", FontSize->24, Background->RGBColor[0, 1, 1]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Integrate[\ Sin[t]/t, \ {t, 0, z}\ ]\ // \ TraditionalForm\)], "Input",\ FontSize->18, CellTags->"Si"], Cell[BoxData[ \(TraditionalForm \`If[z > 0, Si(z), \[Integral]\_0\%z\(\( sin(t)\)\/t\)\[DifferentialD]t] \)], "Output", FontSize->24, Background->RGBColor[0, 1, 1]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Chapter 6: Gamma Function and Related Functions", "Section", CellTags->"Gamma"], Cell[BoxData[ \(Integrate[\ t\^\(z - 1\)\ E\^\(-t\), \ {t, 0, \[Infinity]}\ ]\ // \ TraditionalForm\)], "Input", FontSize->18], Cell[BoxData[ FormBox[ RowBox[{"If", "[", RowBox[{ \(Re(z) > 0\), ",", " ", \(\[CapitalGamma](z)\), ",", " ", RowBox[{ SubsuperscriptBox["\[Integral]", "0", InterpretationBox["\[Infinity]", DirectedInfinity[ 1]]], \(\(\[ExponentialE]\^\(-t\)\ t\^\(z - 1\)\)\[DifferentialD]t \)}]}], "]"}], TraditionalForm]], "Input", TextAlignment->Center, FontSize->24, Background->RGBColor[0, 1, 0]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[\ {Gamma[x], \ 1/Gamma[x]}, \ {x, \(-4\), 4}, \ PlotRange -> {\(-4\), 4}, \n\t\t\tPlotStyle -> {{}, {Dashing[{0.01}]}}, \ PlotLabel -> StyleForm["\[CapitalGamma](x) and 1/\[CapitalGamma](x)", \ FontSize -> 18, \ FontColor -> Hue[0.65]]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.119048 0.309017 0.0772542 [ [.02381 .29652 -6 -9 ] [.02381 .29652 6 0 ] [.2619 .29652 -6 -9 ] [.2619 .29652 6 0 ] [.7381 .29652 -3 -9 ] [.7381 .29652 3 0 ] [.97619 .29652 -3 -9 ] [.97619 .29652 3 0 ] [.4875 0 -12 -4.5 ] [.4875 0 0 4.5 ] [.4875 .07725 -12 -4.5 ] [.4875 .07725 0 4.5 ] [.4875 .15451 -12 -4.5 ] [.4875 .15451 0 4.5 ] [.4875 .23176 -12 -4.5 ] [.4875 .23176 0 4.5 ] [.4875 .38627 -6 -4.5 ] [.4875 .38627 0 4.5 ] [.4875 .46353 -6 -4.5 ] [.4875 .46353 0 4.5 ] [.4875 .54078 -6 -4.5 ] [.4875 .54078 0 4.5 ] [.4875 .61803 -6 -4.5 ] [.4875 .61803 0 4.5 ] [.5 .63053 -84.5 0 ] [.5 .63053 84.5 18 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .30902 m .02381 .31527 L s [(-4)] .02381 .29652 0 1 Mshowa .2619 .30902 m .2619 .31527 L s [(-2)] .2619 .29652 0 1 Mshowa .7381 .30902 m .7381 .31527 L s [(2)] .7381 .29652 0 1 Mshowa .97619 .30902 m .97619 .31527 L s [(4)] .97619 .29652 0 1 Mshowa .125 Mabswid .08333 .30902 m .08333 .31277 L s .14286 .30902 m .14286 .31277 L s .20238 .30902 m .20238 .31277 L s .32143 .30902 m .32143 .31277 L s .38095 .30902 m .38095 .31277 L s .44048 .30902 m .44048 .31277 L s .55952 .30902 m .55952 .31277 L s .61905 .30902 m .61905 .31277 L s .67857 .30902 m .67857 .31277 L s .79762 .30902 m .79762 .31277 L s .85714 .30902 m .85714 .31277 L s .91667 .30902 m .91667 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .5 0 m .50625 0 L s [(-4)] .4875 0 1 0 Mshowa .5 .07725 m .50625 .07725 L s [(-3)] .4875 .07725 1 0 Mshowa .5 .15451 m .50625 .15451 L s [(-2)] .4875 .15451 1 0 Mshowa .5 .23176 m .50625 .23176 L s [(-1)] .4875 .23176 1 0 Mshowa .5 .38627 m .50625 .38627 L s [(1)] .4875 .38627 1 0 Mshowa .5 .46353 m .50625 .46353 L s [(2)] .4875 .46353 1 0 Mshowa .5 .54078 m .50625 .54078 L s [(3)] .4875 .54078 1 0 Mshowa .5 .61803 m .50625 .61803 L s [(4)] .4875 .61803 1 0 Mshowa .125 Mabswid .5 .01545 m .50375 .01545 L s .5 .0309 m .50375 .0309 L s .5 .04635 m .50375 .04635 L s .5 .0618 m .50375 .0618 L s .5 .09271 m .50375 .09271 L s .5 .10816 m .50375 .10816 L s .5 .12361 m .50375 .12361 L s .5 .13906 m .50375 .13906 L s .5 .16996 m .50375 .16996 L s .5 .18541 m .50375 .18541 L s .5 .20086 m .50375 .20086 L s .5 .21631 m .50375 .21631 L s .5 .24721 m .50375 .24721 L s .5 .26266 m .50375 .26266 L s .5 .27812 m .50375 .27812 L s .5 .29357 m .50375 .29357 L s .5 .32447 m .50375 .32447 L s .5 .33992 m .50375 .33992 L s .5 .35537 m .50375 .35537 L s .5 .37082 m .50375 .37082 L s .5 .40172 m .50375 .40172 L s .5 .41717 m .50375 .41717 L s .5 .43262 m .50375 .43262 L s .5 .44807 m .50375 .44807 L s .5 .47898 m .50375 .47898 L s .5 .49443 m .50375 .49443 L s .5 .50988 m .50375 .50988 L s .5 .52533 m .50375 .52533 L s .5 .55623 m .50375 .55623 L s .5 .57168 m .50375 .57168 L s .5 .58713 m .50375 .58713 L s .5 .60258 m .50375 .60258 L s .25 Mabswid .5 0 m .5 .61803 L s gsave .5 .63053 -145.5 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 26 translate 1 -1 scale 63.000000 17.000000 moveto /Courier findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 17.000000 moveto /Math1Mono findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor (G) show /Math2Mono findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor 74.000000 17.000000 moveto (H) show 85.000000 17.000000 moveto /Courier findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor (x) show /Math2Mono findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor 96.000000 17.000000 moveto (L) show 118.000000 17.000000 moveto /Courier findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor (and) show 162.000000 17.000000 moveto (1) show /Math2Mono findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor 173.000000 17.000000 moveto (\\220) show 184.000000 17.000000 moveto /Math1Mono findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor (G) show /Math2Mono findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor 195.000000 17.000000 moveto (H) show 206.000000 17.000000 moveto /Courier findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor (x) show /Math2Mono findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor 217.000000 17.000000 moveto (L) show 228.000000 17.000000 moveto /Courier findfont 18.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.099992 1.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02514 .61803 m .02605 .4847 L .02729 .42424 L .02846 .39668 L .02954 .38122 L .03053 .37138 L .03163 .3635 L .03279 .35726 L .03395 .35246 L .0352 .34842 L .03746 .34306 L .03884 .34061 L .04016 .3387 L .04262 .33588 L .045 .33385 L .04753 .33221 L .04993 .33103 L .0521 .33018 L .05466 .32941 L .056 .32909 L .05743 .3288 L .05867 .32858 L .06004 .32839 L .06129 .32825 L .06244 .32814 L .0638 .32805 L .06451 .32801 L .06527 .32798 L .06654 .32796 L .06727 .32795 L .06795 .32796 L .06921 .32798 L .07036 .32803 L .07163 .3281 L .07296 .3282 L .07575 .3285 L .07835 .32887 L .08119 .3294 L .08424 .33011 L .08972 .33181 L .09489 .33402 L .09954 .33666 L .10458 .34046 L .10947 .34548 L .11404 .35197 L .11667 .35683 L .11906 .36229 L .12183 .37025 L .12446 .38015 L .12699 .39293 L Mistroke .12837 .40191 L .12968 .41213 L .1309 .42377 L .13222 .4394 L .13342 .45747 L .13452 .47871 L .13584 .51299 L .13707 .55914 L .13778 .59579 L Mfstroke .13778 .59579 m .13811 .61803 L s .14297 .61803 m .14302 0 L s .14816 0 m .14923 .05054 L .15047 .08956 L .15163 .11574 L .15269 .13434 L .15509 .16421 L .15635 .17547 L .15752 .18418 L .16019 .19938 L .16279 .21 L .16558 .21839 L .16829 .22452 L .17124 .22953 L .17403 .2331 L .17662 .23561 L .17894 .23733 L .1815 .23873 L .18279 .23926 L .18418 .23971 L .18549 .24003 L .18669 .24024 L .18796 .24036 L .18917 .2404 L .19025 .24038 L .19142 .24028 L .1927 .24009 L .19334 .23996 L .19405 .2398 L .19648 .23906 L .19875 .23809 L .20118 .23676 L .20559 .23352 L .20824 .23101 L .21113 .22773 L .2164 .22003 L .22153 .20979 L .22628 .19693 L .23137 .17793 L .23423 .16376 L .23686 .14759 L .23937 .12841 L .2417 .10596 L .24414 .07593 L .24682 .03138 L .24798 .00666 L s .24798 .00666 m .24824 0 L s .26217 0 m .26218 .61803 L s .27962 .61803 m .28051 .60488 L .28306 .5772 L .28546 .55716 L .28771 .5422 L .29009 .52949 L .29434 .51253 L .2967 .50555 L .29891 .50029 L .30133 .4957 L .30392 .49199 L .30649 .48937 L .30779 .48842 L .30854 .48798 L .30923 .48765 L .31045 .4872 L .31176 .48694 L .31297 .48689 L .31413 .48702 L .31483 .48717 L .31546 .48736 L .31688 .48797 L .31819 .48875 L .31943 .48968 L .32221 .49247 L .32521 .49661 L .33031 .50656 L .33288 .51317 L .3357 .52185 L .34069 .54166 L .34535 .56686 L .35035 .60429 L s .35035 .60429 m .35174 .61803 L s .38176 .61803 m .38178 0 L s .421 0 m .42127 .00123 L .424 .01115 L .42655 .01862 L .42893 .02416 L .4314 .02864 L .4328 .03062 L .43411 .03215 L .43524 .03321 L .43646 .0341 L .43757 .03467 L .43859 .03501 L .4397 .03517 L .44091 .0351 L .44219 .03476 L .44337 .03419 L .44467 .03328 L .44607 .03196 L .44863 .02861 L .45113 .02414 L .45344 .01883 L .45867 .00205 L s .45867 .00205 m .45914 0 L s .50014 0 m .50016 .61803 L s .52732 .61803 m .52848 .60245 L .53112 .5762 L .53401 .55233 L .53913 .51903 L .54389 .49538 L .54894 .47563 L .55442 .45868 L .56436 .43595 L .57403 .42035 L .58295 .4097 L .59264 .40092 L .60171 .39464 L .61167 .38935 L .62236 .38509 L .63249 .38212 L .63784 .3809 L .64354 .37983 L .64901 .37901 L .65397 .37843 L .65895 .37799 L .66138 .37782 L .66364 .37769 L .6659 .37759 L .66831 .37751 L .66969 .37748 L .67099 .37745 L .67216 .37744 L .67343 .37743 L .67467 .37743 L .67538 .37744 L .67604 .37744 L .67673 .37745 L .67737 .37746 L .6788 .37749 L .68002 .37752 L .68135 .37756 L .68376 .37765 L .6884 .3779 L .69335 .37827 L .70225 .3792 L .71252 .38067 L .72364 .38277 L .74381 .38791 L .76373 .39485 L .78479 .40449 L .80441 .416 L .82273 .4294 L .86162 .46902 L .88284 .49928 L Mistroke .90295 .53563 L .92152 .57765 L Mfstroke .92152 .57765 m .93574 .61803 L s [ .01 ] 0 setdash .02381 .30902 m .03279 .43272 L .04262 .53117 L .04758 .56658 L .0503 .58219 L .05288 .59452 L .05528 .60395 L .05789 .61204 L .05904 .61492 L .06026 .61753 L s .06026 .61753 m .06054 .61803 L s .07423 .61803 m .07519 .6165 L .07742 .61185 L .0825 .59779 L .08807 .57761 L .09315 .55578 L .10458 .49884 L .12528 .38874 L .13438 .34484 L .14443 .30301 L .15337 .27281 L .16301 .24828 L .16832 .23834 L .17319 .23139 L .17785 .22662 L .18019 .22489 L .18153 .22409 L .18275 .22347 L .18396 .22298 L .18529 .22255 L .18598 .22238 L .18663 .22226 L .18731 .22215 L .18804 .22208 L .18868 .22204 L .18938 .22203 L .19065 .2221 L .19188 .22227 L .19303 .22251 L .19425 .22285 L .1954 .22326 L .19755 .22422 L .20237 .22728 L .20761 .23188 L .21244 .23708 L .22332 .25142 L .24378 .28284 L .26286 .31024 L .27229 .32132 L .28122 .32979 L .28615 .33356 L .29151 .3369 L .29638 .33925 L .30088 .34086 L .30331 .3415 L .30553 .34195 L .30679 .34215 L .30797 .3423 L .30919 .34243 L .30984 .34247 L Mistroke .31053 .34252 L .3117 .34256 L .31297 .34257 L .31417 .34254 L .31528 .34249 L .31627 .34242 L .31737 .34232 L .31958 .34203 L .32227 .34154 L .32472 .34096 L .33024 .33925 L .3402 .33492 L .35926 .32355 L .38001 .30963 L .39937 .29817 L .4104 .29316 L .41544 .29133 L .42076 .28976 L .42546 .28867 L .42794 .28822 L .4306 .28783 L .43305 .28755 L .43528 .28738 L .43635 .28731 L .43752 .28726 L .43862 .28724 L .43963 .28722 L .4408 .28723 L .44206 .28725 L .44325 .2873 L .44434 .28735 L .44561 .28744 L .447 .28756 L .44952 .28784 L .45215 .28823 L .45495 .28874 L .45999 .28991 L .47029 .29328 L .48142 .29824 L .5016 .31006 L .54262 .34008 L .58213 .36779 L .602 .37886 L .62012 .38667 L .63015 .38999 L .63964 .39246 L .64967 .39439 L .65533 .39517 L .65806 .39546 L .66056 .39569 L Mistroke .66278 .39586 L .6652 .39601 L .66764 .39613 L .66897 .39617 L .6702 .39621 L .67138 .39623 L .67249 .39624 L .67349 .39625 L .67457 .39625 L .67575 .39624 L .677 .39622 L .67807 .3962 L .67924 .39617 L .68193 .39607 L .68438 .39594 L .68989 .39553 L .695 .39501 L .69985 .3944 L .70947 .39287 L .71971 .39083 L .73811 .38627 L .77977 .37323 L .81991 .35954 L .85853 .34723 L .89961 .33615 L .93917 .32778 L .97619 .32189 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{481, 297.125}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHge]M3oo`00<`00_k:b/ZOL000<10000 m`000>L000<10000m`0005D000<10040:P000`40000300030@00034000<100003P000`40000>0003 0@0000<01@4700<1kP0005D000<10040:P000`40000300030@00034000<100003P000`40000>00D1 00D00@000@0800030@000>h0001E00030@0102X000<100000`000`40000a00030@0000l000<10000 3@000`40000400030@0100P000<10000kP0005D000<10040:P000`40000300030@00034000<10000 3`000`40000<00030@0000H00P4800030@000>h0001E00030@0102X000<100000`000`40000a0003 0@00010000<100002`000`40000700030@0000H000<10000kP0005D000<10040:P000`4000030003 0@00034000<1000040000`40000:00030@00014000<10000kP0005D000<10040:P000`4000030003 0@00034000<1000040000`40000:00030@00014000<10000kP0005D000<10040:P000`4000030003 0@00034000<100004@000`40000800030@0001800P7_0000E@000`400@0Z00030@0000<000<10000 <@000`40000A00030@0000P000<100004P000`40003^0000E@000`400@0Z00030@0000<000<10000 <@000`40000B00030@0000L000<100004P000`40003^0000E@000`400@0Z00030@0000<000<10000 <@000`40000B00030@0000H000<100004`000`40003^0000E@000`400@0Z00030@0000<000<10000 <@000`40000C00030@0000D000<100004`000`40003^0000E@000`400@0Z00030@0000<000<10000 <@000`40000C00030@0000@000<1000050000`40003^0000E@000`400@0Z00030@0000<000<10000 <@000`40000C00030@0000@000<1000050020Nl0001E00030@0102X000<100000`000`40000a0003 0@0001@000@100000P4G00030@000>h0001E00030@0102X000<100000`000`40000a00030@0001D0 104H00030@000>h0001E00030@0102X000<100000`000`40000a00030@00034000<10000kP0005D0 00<10040:P000`40000300030@00034000<10000<@000`40003^0000E@000`400@0Z00030@0000<0 00<10000<@000`40000a00030@000>h0001E00030@0102T000<1000010000`40000a00030@000340 00<10000kP0005D000<10040:@000`40000400030@00034000<10000<@020Nl0001E00030@0102T0 00<1000010000`40000a00030@00034000<10000kP0005D000<10040:@000`40000400030@000340 00<10000<@000`40003^0000E@000`400@0Y00030@0000@000<10000<@000`40000a00030@000>h0 001E00030@0102T000<1000010000`40000a00030@00034000<10000kP0005D000<10040:@000`40 000400030@00034000<10000<@000`40003^0000E@000`400@0Y00030@0000@000<10000<@000`40 000a00030@000>h0001E00030@0102T000<1000010000`40000a00030@0003400P7_0000E@000`40 0@0Y00030@0000@000<10000<@000`40000a00030@000>h0001E00030@0102P000<100001@000`40 000a00030@00034000<10000kP0005D000<10040:0000`40000500030@00034000<10000<@000`40 003^0000E@001040004W00030@0000D000<10000<@000`40000W008120000`40003^0000E@001040 004W00030@0000D000<10000<@000`40000V00040@000@L000<10000kP0005D000@100019`000`40 000500030@00034000<10000:@000`40000500<1kP0005D000@100019`000`40000500030@000340 00<1000080040@<00P4800030@000>h0001E00040@000BL000<100001@000`40000a00030@0002T0 00<100001@000`40003^0000E@001040004W00030@0000D000<10000<@000`40000V00040@000@L0 00<10000kP0005D000@100019`000`40000500030@00034000<100009`020@P000<10000kP0005D0 00@100019`000`40000500030@00034000<10000<@000`40003^0000E@001040004W00030@0000D0 00<10000<@000`40000a00030@000>h0001E00040@000BH000<100001P000`40000a00030@000340 0P7_0000E@001040004V00030@0000H000<10000<@000`40000a00030@000>h0001E00040@000BH0 00<100001P000`40000a00030@00034000<10000kP0005D000@100019P000`40000600030@000340 00<10000<@000`40003^0000E@001040004V00030@0000H000<10000<@000`40000a00030@000>h0 001E00040@000BH000<100001P000`40000a00030@00034000<10000kP0005D000@100019P000`40 000600030@00034000<10000<@000`40003^0000E@001040004V00030@0000H000<10000<@000`40 000a0081k`0005D000@100019P000`40000600030@00034000<10000<@000`40003^0000E@001040 004V00030@0000H000<10000<@000`40000a00030@000>h0001E00040@000BH000<100001P000`40 000a00030@00034000<10000kP0005D000@100019P000`40000600030@00034000<10000<@000`40 003^0000E@001040004U00030@0000L000<10000<@000`40000a00030@000>h0001E00040@000BD0 00<100001`000`40000a00030@00034000<10000kP0005D000D100000@0T00030@0000L000<10000 <@000`40000a0081k`0005D000D100000@0T00030@0000L000<10000<@000`40000a00030@000>h0 001E00050@00004090000`40000700030@00034000<10000<@000`40003^0000E@001@40000102@0 00<100001`000`40000a00030@00034000<10000kP0005D000D100000@0T00030@0000L000<10000 <@000`40000a00030@000>h0001E00050@00004090000`40000700030@00034000<10000<@000`40 003^0000E@001@40000102@000<100001`000`40000a00030@0003400P7_0000E@001@40000102<0 00<1000020000`40000a00030@00034000<10000kP0005D000D100000@0S00030@0000P000<10000 <@000`40000a00030@000>h0001E00050@0000408`000`40000800030@00034000<10000<@000`40 003^0000E@001@40000102<000<1000020000`40000a00030@00034000<10000kP0005D000<10000 0P000`40000P00030@0000P000<10000<@000`40000V00@11`000`40003^0000E@000`4000020003 0@00020000<1000020000`40000a00030@0002H000<1000020000`40003^0000E@000`4000020003 0@00020000<1000020000`40000a00030@0002L000<100001`030Nh0001E00030@00008000<10000 7`000`40000900030@00034000<1000080040@@000<100001P000`40003^0000E@000`4000020003 0@0001l000<100002@000`40000a00030@0002T000<100001@000`40003^0000E@000`4000020003 0@0001l000<100002@000`40000a00030@0002H000@100011`000`40003^0000E@000`4000020003 0@0001l000<100002@000`40000a00030@0002L00P4800030@000>h0001E00030@00008000<10000 7`000`40000900030@00034000<10000<@000`40003^0000E@000`40000200030@0001l000<10000 2@000`40000a00030@00034000<10000kP0005D000<100000P000`40000O00030@0000T000<10000 <@000`40000a0081k`0005D000<100000P000`40000N00030@0000X000<10000<@000`40000a0003 0@000>h0001E00030@00008000<100007P000`40000:00030@00034000<10000<@000`40003^0000 E@000`40000200030@0001h000<100002P000`40000a00030@00034000<10000kP0005D000<10000 0`000`40000M00030@0000X000<10000<@000`40000a00030@000>h0001E00030@0000<000<10000 7@000`40000:00030@00034000<10000<@000`40003^0000E@000`40000300030@0001`000<10000 2`000`40000a00030@0003400P7_0000E@000`40000300030@0001`000<100002`000`40000a0003 0@00034000<10000kP0005D000<100000`000`40000L00030@0000/000<10000<@000`40000a0003 0@000>h0001E00030@0000@000<100006`000`40000;00030@00034000<10000<@000`40003^0000 E@000`40000400030@0001X000<1000030000`40000a00030@00034000<10000kP0005D000<10000 10000`40000J00030@0000`000<10000<@000`40000a00030@000>h0001E00030@0000@000<10000 6P000`40000<00030@00034000<10000<@000`40003^0000E@000`40000400030@0001T000<10000 3@000`40000a00030@0003400P7_0000E@000`40000400030@0001T000<100003@000`40000a0003 0@00034000<10000kP0005D000<100001@000`40000H00030@0000d000<10000<@000`40000a0003 0@000>h0001E00030@0000D000<100005`000`40000>00030@00034000<10000<@000`40003^0000 E@000`40000500030@0001L000<100003P000`40000a00030@00034000<10000kP0005D000<10000 1@000`40000F00030@0000l000<10000<@000`40000a00030@000>h0001E00030@0000H000<10000 5@000`40000?00030@00034000<10000<@000`40003^0000E@000`40000600030@0001@000<10000 40000`40000a00030@0003400P7_0000E@000`40000600030@0001<000<100004@000`40000a0003 0@00034000<10000kP0005D000<100001`000`40000800030@0000L000<100004@000`40000a0003 0@00034000<10000kP0005D000<1000020000`400002008110020@H000<100004P000`40000a0003 0@00034000<10000kP0005D000<100002@0010400048008110000`40000B00030@00034000<10000 9P040@L000<10000kP0005D000<100002@000`400@0>00030@0001<000<10000<@000`40000X0003 0@0000H000<10000kP0005D000<100002P000`40000<00030@0001@000<10000<@000`40000X0003 0@0000H00`7^0000E@000`40000:00030@0000/00P4F00030@00034000<1000080040@@000<10000 1P000`40003^0000E@000`40000;00030@0000T000@100015@000`40000a00030@0002P000<10000 1P000`40003^0000E@000`40000800040@0000811`020@@000<100004P000`40000a00030@0002H0 0`4800030@000>h0001E00030@0000P000<100000`070@L000<100004@000`40000a00030@0002P0 00<100001P000`40003^0000E@000`40000700030@00018000<100004@000`40000a00030@000340 00<10000kP0005D000<100001`000`40000V00030@00034000<10000<@000`40003^0000E@000`40 000600030@0002L000<10000<@000`40000a0081k`0005D000<100007`000`40000>00030@000340 00<10000<@000`40003^0000E@000`40000O00030@0000h000<10000<@000`40000a00030@000>h0 001E00030@00020000<100003@000`40000a00030@00034000<10000kP0005D000<1000010000`40 000I00030@0000d000<10000<@000`40000a00030@000>h0001E00030@0000@000<100006P000`40 000<00030@00034000<10000<@000`40003^0000E@000`40000400030@0002T000<10000<@000`40 000a00030@000>h0001E00030@0000<000<10000:P000`40000a00030@0003400P7_0000E@000`40 000300030@0001h000<100002@000`40000a00030@00034000<10000kP0005D000<100009@000`40 000800030@00034000<10000<@000`40003^0000E@000`40000U00030@0000P000<10000<@000`40 000a00030@000>h0001E00030@0002H000<100001`000`40000a00030@00034000<10000kP0005D0 00D100000@0T00030@0000L000<10000<@000`40000a00030@000>h0001E00050@000040;P000`40 000a00030@00034000<10000kP0005D000D100000@0^00030@00034000<10000<@020Nl0000T0003 0@0002h000@10001;`050Bl000<10000<@000`40001R00@1I@000`40000P000090000`40000^0004 0@000BL000<100001@020C8000<10000<@000`40001R00030@0006H000<10000800002401@4_0003 0@0002T000<1000010000`400@0a00030@00034000<10000H`000`40001R00D18@0001`010401@01 0001030000<10000:P050@0500400040<0000`40000A00D10`060A8000<10000I0000`40001Q0004 0@000B80000R00030@01030000<10000:`000`40000200050@000040;`000`40000;008190000`40 001U00030@00064000<100408P0002<00P4`0081<@020@8000<10000;@000`40000900815`030@`0 0P5S00040@000F@00P4R000090000`40000^0081<@0010400@4`00030@0000P000<100006P020@X0 00<10000H`020FH000<10000800005D00P4a00030@00034000<10000<@000`40003^0000E@000`40 000]00040@000C<000<1000010000`40000S00030@0000@000<10000kP0005D000<10000;P000`40 0@0c00030@0000800P4W008110000`40003^0000E@000`40000_0081<`001@40000102/000D10000 0@3`0000E@000`40000`00030@00034000<10000<@000`40003^00005`3o0K<16000024000<10000 5`000`40000F008160000`40000G00030@0001L000<1000050020@03004001P000<100005`020AL0 00<100005`000`40000G00030@0001L000<100005`000`40000F00030@0001L000<100005`000`40 000P00008@000`40000G00030@0001H00P4H00030@0001L000<100005`000`40000C00050@000040 6@000`40000G00040@010AD000<100005`000`40000G00030@0001L000<100005`000`40000F0003 0@0001L000<100005`000`40000P00008@000`40000`0081h0001C00030@01038000<100000P000`40000T00811P000`40000a00030@000>h0001C0003 0@01038000<100000P000`40000R008120000`40000a00030@0000@000<10000`0030B@0001E0003 0@00030000<100009P000`40000800030@0003400P460081]`030@@00P4W0000<0080Ad000<10000 <0000`40000a00030@00034000<100001`020K<00P4`00008@000`40000900<120040AT000<10000 <0000`40000500816`000`40000<00030@00034000<10000]P030CD0000Q00030@0000L00P4?00<1 4`001040004b00030@0000L000<100005P020@l000<10000<@000`40002c00<1>000028000<10000 1@000`40000B00814@001040004b00030@0000P00P4E00030@0000l000<10000<@000`40000;0003 0@0009l00`4n00008P000`40000400030@0001D00P4?00040@000C8000<10000<@000`40000a0003 0@0000`00P6M0081@@00028000<100000`000`40000H00030@0000/000D100000@0b00030@0000d0 00<100002P020AD000<10000<@020@l00P6E00<1AP0002L000<100006P000`40000:00050@000040 00D10`040AL000<10000<@000`40002S0081B@0002L000<100006`000`40000=0003 0@00030000<100004P000`40000L00030@00034000<10000W0030Dl0000W00030@0001`000<10000 30000`40000`00030@00034000<10000<@000`40000B00030@0008D00P5B00008P001@4000010200 00<100002`000`40000`00030@00034000<10000<@000`40000C0081P0020EL0000R00050@000040 80000`40000600030@00008000<10000<0000`40000a00030@00034000<100005@020G`00P5I0000 8P001040004R00030@0000D000<100000P000`40000`00030@00034000<10000<@000`40002B0003 0@0005T0000R00040@000B<000<1000010000`40000200030@00030000<10000<@000`40000a0081 S@030El0000R00040@000B<000<100000`000`40000300030@00030000<10000<@000`40000a0003 0@0001T000<10000KP020F80000R00040@000B@000<100000P000`40000300030@00030000<10000 <@000`40000a00030@0001X00P7B000090000`40000S00030@00008000<100000`000`40000`0003 0@00034000<10000<@000`40000L0081IP030FL0000T00030@0002<000<1000020000`40000`0003 0@00034000<10000<@000`40002100<1JP0002@000<1000090000`40000700030@00030000<10000 <@000`40000a00030@0007`00P5`00008`020BH000<100001`000`40000`00030@00034000<10000 <@000`40000P00030@0005L00P5b00008`020BH000D100000@0500030@00030000<10000<@000`40 000a00818P020EH000<10000LP0002<00P4W00040@000@D000<10000<0000`40000a00030@000340 00<100008`020Dh00`5h00008`020BL000@100011@000`40000`00030@00034000<10000<@000`40 001a0081N`0002<000<100009`020@H000<10000<0000`40000a00030@00034000<10000:0020A80 6`6G00008`000`40000W00811P000`40000`00030@00034000<100009P040@L000<10000:P020@/0 1@4K00D13`030H00000S00030@0002L000<100001@000`40000`00030@00034000<10000:0000`40 000600030@0002`000<100001@030BD010490081P`0002<000<100009`000`40000500030@000300 00<10000<@000`40000X00030@0000H00`4`00@1;0060HP0000S00030@0002P000<1000010000`40 000`00030@00034000<10000:0000`40000600030@0002l0104]00810P040HH0000S00030@0002L0 0P4600030@00030000<10000<@000`40000X00030@0000H000<10000;0030@@00P4U00<12`030H<0 000S00030@0002L00P4600030@00030000<10000<@000`40000V00<120000`40000Z008130030Ad0 0P4A00<1P00002<00P4X00811P000`40000`00030@00034000<10000:0000`40000600030@0002T0 00<100003`020@@000<1000030050AT00`5m00008`020BL000<100401P000`40000`00030@000340 00<10000<@000`40000W00816@000`40000200D10`000`40000O0081N`0002<00P4W00030@0100H0 00<10000<0000`40000a00030@00034000<100009P000`40001:0081N@0002<000<100009P000`40 0@0600030@00030000<10000<@000`40000a00819P000`40001=0081M`0002<000<10000:0000`40 000400030@00030000<10000<@000`40000a00030@0002@000<10000D0020GD0000S00030@0002P0 00<1000010000`40000`00030@00034000<10000<@000`40000R0081E@020G<0000S0081:P000`40 000300030@00030000<10000<@000`40000a00030@00024000<10000E`020G40000S00819P001@40 000100D000<10000<0000`40000a00030@00034000<1000080000`40001J0081K`00028000<10040 9P001@40000100D000<10000<0000`40000a00030@00034000<100007`000`40001M0081K@000280 00<100409P001@40000100D000<10000<0000`40000a00030@00034000<100007`000`40001O0003 0@0006X0000R00030@0102D000<100000P000`40000300030@00030000<10000<@000`40000a0081 7`000`40001Q00030@0006T0000R00030@0102D000<100000P000`40000300030@00030000<10000 <@000`40000a00030@0001d000<10000H`020FT0000R00030@0002X000<100000`000`40000`0003 0@00034000<10000<@000`40000L00030@0006H000<10000IP00028000<10000:P000`4000030003 0@00030000<10000<@000`40000a00030@0001`000<10000I`000`40001U00008P000`40000Z0003 0@0000<000<10000<0000`40000a00030@00034000<100006`000`40001Y0081I@00028000@10001 90000`40000200030@0000<000<10000<0000`40000a00030@00034000<100006P000`40001/0003 0@000680000R00040@000B@000<100000P000`40000300030@00030000<10000<@000`40000a0003 0@0001T000<10000KP000`40001Q00008P001040004T00030@0000<000<100000P000`40000`0003 0@00034000<10000<@020AX000<10000K`000`40001P00008P001040004S00030@0000@000<10000 0P000`40000`00030@00034000<10000<@000`40000H00030@00074000<10000G`00028000@10001 8`000`40000400030@00008000<10000<0000`40000a00030@00034000<1000060000`40001b0003 0@0005h0000R00030@0002@000<1000010000`40000200030@00030000<10000<@000`40000a0003 0@0001L000<10000M0000`40001M00008P000`40000[00030@00008000<10000<0000`40000a0003 0@00034000<100005`000`40001e00030@0005`0000R00030@0002/000<100000P000`40000`0003 0@00034000<10000<@000`40000F00030@0007L000<10000F`00028000<10000:`000`4000020003 0@00030000<10000<@000`40000a00815`000`40001h00030@0005X0000R00040@000B8000<10000 1@000`40000200030@00030000<10000<@000`40000a00030@0001H000<10000N0000`40001J0000 8P001040004R00030@0000D000<100000P000`40000`00030@00034000<10000<@000`40000E0003 0@0007X000<10000F@00028000D100000@0Q00030@0000D000<100000P000`40000`00030@000340 00<10000<@000`40000E00030@0007/000<10000F000028000D100000@0P00030@0000H000<10000 0P000`40000`00030@00034000<10000<@000`40000D00030@0007d000<10000E`00028000D10000 0@0P00030@0000H000<100000P000`40000`00030@00034000<100009P040@L000<1000050000`40 001n00030@0005H0000R00030@0002/000<100000P000`40000`00030@00034000<100009P000`40 000800030@0001@000<10000O`000`40001E00008P000`40000[00030@00008000<10000<0000`40 000a00030@0002L000<100001`030A<000<10000P@000`40001D00008P000`40000[00030@000080 00<10000<0000`40000a00030@0002P000<100001P000`40000C00030@00088000<10000D`000280 00D100000@0O00030@0000P000D100000@0b00030@00034000<10000:@000`40000500030@0001<0 00<10000P`000`40001B00008P001@40000101l000<1000020001@400001038000<10000<@000`40 000V00040@000@L000<100004`000`40002400030@000540000R00050@0000407`000`4000080005 0@00004000030@000180 00<10000<@000`40000>00030@0009D000<10000A@00028000<100000`000`40000G00030@0000`0 00D100000@0b00030@0000/000<100003P000`40000B00030@00034000<100003@000`40002G0003 0@0004@0000R00030@0000<000<100005`000`40000<00050@0000400003 0@0002H000@100011`000`40000;00030@000:0000<10000?@00028000<100001@000`40000C0003 0@0000l000@1000100030@0003400P4<0003 0@000:4000<10000?000024000<100001`000`40000A00030@00010000@10001`00024000<10000;P001040004b00030@0000L000<100005`000`40000=00030@00034000<10000 2`000`40002R00030@0003/0000Q00030@0002h000@10001P00024000<100001`000`40000@0003 0@00014000@10001@00024000<1000020000`40000>0003 0@00018000@10001000024000<10000 ;P001040004b00030@0000H000<100006@000`40000<00030@00034000<100002P000`40002W0003 0@0003L0000Q00030@0001P000<100004`001040004b00030@0000H000<100006P000`40000;0003 0@00034000<100002P000`40002W00030@0003L0000Q00030@0000T000<1000030000`40000C0004 0@000C8000<100001P000`40000J00030@0000/000<10000<@020@/000<10000Z0000`40000f0000 8@000`40000900030@0000`000<100004`001040004b00030@0000H000<100006P000`40000;0003 0@00034000<100002@000`40002Y00030@0003H0000Q00030@0000T000<100002`000`40000D0004 0@000C8000<100001@000`40000K00030@0000/000<10000<@000`40000900030@000:T000<10000 =P00024000<100002@000`40000;00030@0001@000@1000180 003o0>80002^00032000014000<80000HP000`P0000A000320000:<0002]0003200001<000<80000 H0000`P0000C000320000:80002]0003200001<000<80000H0000`P0000C000320000:80002/0003 200001D000<80000GP000`P0000E000320000:40002N00D82@000`P0000500<80P0320P000<80000 3`04200400P820800`P300<81004200300P800h01`P50003200000H01@P90003200000D00`P200<8 20000`P0002Q0000X0000`P000090003200000H000<800000P000`P000070003200000h000<80000 0P0220D000<800000`000`P000020003200000800PPB0003200000H000<8000020000`P000090003 200000H000<800000P000`P00007000320000:40002P0003200000T000<800001`0010P000P:0003 200000h000<800000`000`P000030003200000<000D80000200600032000010000<800001`000`P0 00070003200000T000<800001`0010P000P:000320000:40002P0003200000T000<80000200220/0 00<800003P000`P000030003200000<000<800000`001@P0000800H000<8000040000`P000070003 200000L000<800002@000`P0000800882`000`P0002Q0000X0000`P000090003200000P00PP;0003 200000l01PP50003200000<000D80000200600032000010000<8000020000`P000060003200000T0 00<80000200220/000<80000X@000:0000<800002@000`P000070004200020X000<8000050000`P0 00030003200000<000D80000200600032000010000<8000020000`P000060003200000T000<80000 1`0010P000P:000320000:40002P0003200000T000<800001P000`P000020003200000L000<80000 3`000`P000020003200000<00PP400032000008000<800000P02218000<800002@000`P000050003 200000T000<800001P000`P000020003200000L000<80000X@000:0000<800002@000`P0000500<8 0P0320P000<80000400420D00PP00`08200220H010P00`08000A0003200000T000<800001@000`P0 00090003200000D00`P200<820000`P0002Q0000X0000`P000030003200000@000<800004`000`P0 000/00032000010000<800002P000`P000040003200000<000<8000010000`P0000C000320000:80 002P0003200000<000<8000010000`P0000C0003200002`000<8000040000`P0000:0003200000@0 00<800000`000`P000040003200001<000<80000XP0009h02@P700032000014000<80000;@000`P0 000=008800<02000300010P0000920L000<800004@000`P0002S0000l@0221400PSK0000o`3R0000 \>"], ImageRangeCache->{{{0, 480}, {296.125, 0}} -> {-4.64562, -4.13427, 0.0193567, 0.0298286}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Chapter 7: Error Function and Fresnel Integrals", "Section", CellTags->"Err"], Cell[CellGroupData[{ Cell[BoxData[ \(x\ \ \ = \ \ \ 2\ \ Integrate[Exp[\(-t^2\)], \ {t, 0, z}]\ \ /\ \ Sqrt[Pi]\)], "Input",\ FontSize->18, Background->RGBColor[1, 0, 1]], Cell[BoxData[ \(Erf[z]\)], "Output", TextAlignment->Center, FontSize->18, Background->RGBColor[1, 0, 1]] }, Open ]], Cell[BoxData[ \(Integrate[Exp[\(-a\)\ t^2]Cos[2 x\ t], \n \t\t\t\t\t\t\t\t\t\t\t{t, 0, Infinity}]\)], "Input", FontSize->18, Background->RGBColor[1, 1, 0]], Cell[BoxData[ \(\(E\^\(-\(x\^2\/a\)\)\ \@\[Pi]\)\/\(2\ \@a\)\)], "Input", TextAlignment->Center, FontSize->18, Background->RGBColor[1, 1, 0]] }, Open ]], Cell[CellGroupData[{ Cell["Chapter 9: Bessel Functions of Integer Order", "Section"], Cell[BoxData[ \(\(\ \(x\ \ \ \ = \ \ Sum[\ \((\(-z^2\)/4)\)^n/\((\(n!\))\)^2, \ \ {n, 0, Infinity}\ ]; \)\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \({x, \ TraditionalForm[x]}\)], "Input", FontSize->18], Cell[BoxData[ RowBox[{"{", RowBox[{\(BesselJ[0, \@z\^2]\), ",", TagBox[ FormBox[\(\(J\_0\)(\@z\^2)\), "TraditionalForm"], TraditionalForm, Editable->True]}], "}"}]], "Output", FontSize->24, Background->RGBColor[0, 1, 0]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ \ {BesselJ[0, x], \ BesselY[0, x], \ BesselK[0, x], \ BesselI[0, x]}, \n \t\t\t\t\t{x, 0, 8}, \ PlotRange -> {\(-2\), 3}, \ PlotStyle -> \n \t\t{{}, \ {Hue[0.65]}, \ {Dashing[{0.03}]}, \ {Hue[0], Dashing[{0.005}]}}]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.119048 0.247214 0.123607 [ [.2619 .23471 -3 -9 ] [.2619 .23471 3 0 ] [.5 .23471 -3 -9 ] [.5 .23471 3 0 ] [.7381 .23471 -3 -9 ] [.7381 .23471 3 0 ] [.97619 .23471 -3 -9 ] [.97619 .23471 3 0 ] [.01131 0 -12 -4.5 ] [.01131 0 0 4.5 ] [.01131 .12361 -12 -4.5 ] [.01131 .12361 0 4.5 ] [.01131 .37082 -6 -4.5 ] [.01131 .37082 0 4.5 ] [.01131 .49443 -6 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .61803 -6 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .2619 .24721 m .2619 .25346 L s [(2)] .2619 .23471 0 1 Mshowa .5 .24721 m .5 .25346 L s [(4)] .5 .23471 0 1 Mshowa .7381 .24721 m .7381 .25346 L s [(6)] .7381 .23471 0 1 Mshowa .97619 .24721 m .97619 .25346 L s [(8)] .97619 .23471 0 1 Mshowa .125 Mabswid .08333 .24721 m .08333 .25096 L s .14286 .24721 m .14286 .25096 L s .20238 .24721 m .20238 .25096 L s .32143 .24721 m .32143 .25096 L s .38095 .24721 m .38095 .25096 L s .44048 .24721 m .44048 .25096 L s .55952 .24721 m .55952 .25096 L s .61905 .24721 m .61905 .25096 L s .67857 .24721 m .67857 .25096 L s .79762 .24721 m .79762 .25096 L s .85714 .24721 m .85714 .25096 L s .91667 .24721 m .91667 .25096 L s .25 Mabswid 0 .24721 m 1 .24721 L s .02381 0 m .03006 0 L s [(-2)] .01131 0 1 0 Mshowa .02381 .12361 m .03006 .12361 L s [(-1)] .01131 .12361 1 0 Mshowa .02381 .37082 m .03006 .37082 L s [(1)] .01131 .37082 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(2)] .01131 .49443 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(3)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .02472 m .02756 .02472 L s .02381 .04944 m .02756 .04944 L s .02381 .07416 m .02756 .07416 L s .02381 .09889 m .02756 .09889 L s .02381 .14833 m .02756 .14833 L s .02381 .17305 m .02756 .17305 L s .02381 .19777 m .02756 .19777 L s .02381 .22249 m .02756 .22249 L s .02381 .27193 m .02756 .27193 L s .02381 .29666 m .02756 .29666 L s .02381 .32138 m .02756 .32138 L s .02381 .3461 m .02756 .3461 L s .02381 .39554 m .02756 .39554 L s .02381 .42026 m .02756 .42026 L s .02381 .44498 m .02756 .44498 L s .02381 .46971 m .02756 .46971 L s .02381 .51915 m .02756 .51915 L s .02381 .54387 m .02756 .54387 L s .02381 .56859 m .02756 .56859 L s .02381 .59331 m .02756 .59331 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .37082 m .02499 .37082 L .02605 .37081 L .02729 .37079 L .02846 .37077 L .03053 .37072 L .03279 .37064 L .03527 .37053 L .0379 .37039 L .04262 .37005 L .04749 .3696 L .05205 .36909 L .06244 .36759 L .07305 .36559 L .08274 .36336 L .10458 .357 L .14429 .34114 L .18248 .32173 L .22313 .29824 L .26226 .27468 L .30384 .25062 L .34391 .23022 L .38246 .21454 L .40239 .20829 L .41256 .20563 L .42346 .20318 L .43373 .20127 L .4431 .19987 L .45251 .19878 L .45711 .19836 L .46143 .19804 L .46602 .19777 L .46846 .19766 L .47108 .19757 L .47369 .1975 L .475 .19747 L .47575 .19746 L .47643 .19745 L .47766 .19744 L .47898 .19743 L .48019 .19743 L .48134 .19743 L .4824 .19744 L .48357 .19745 L .4848 .19747 L .48594 .19749 L .48798 .19754 L .49018 .19761 L .49519 .19783 L .49976 .19811 L Mistroke .50963 .19894 L .51878 .19998 L .53952 .20329 L .56008 .20773 L .5787 .2126 L .61882 .22518 L .65742 .2388 L .69848 .2533 L .73802 .26581 L .77604 .27536 L .79559 .27903 L .81652 .28193 L .82672 .28294 L .8321 .28336 L .8378 .28372 L .84278 .28396 L .84542 .28407 L .84826 .28416 L .85087 .28422 L .85201 .28425 L .85326 .28427 L .85436 .28428 L .85554 .28429 L .85678 .2843 L .85793 .28431 L .85917 .28431 L .85988 .28431 L .86053 .28431 L .86123 .2843 L .86186 .2843 L .86328 .28429 L .86449 .28427 L .86581 .28425 L .8682 .2842 L .871 .28412 L .87398 .28402 L .87932 .28378 L .8889 .28316 L .89948 .28222 L .91881 .27983 L .93965 .27636 L .97619 .26843 L Mfstroke 0 .1 1 r .02967 0 m .03053 .01218 L .03279 .03509 L .03527 .05452 L .0379 .07105 L .04262 .09434 L .05205 .1277 L .06244 .15414 L .0842 .19358 L .10458 .22067 L .14335 .25852 L .16449 .27398 L .18458 .28594 L .20461 .29543 L .22277 .30204 L .23222 .30477 L .24244 .30719 L .25324 .30915 L .2585 .30989 L .26341 .31046 L .268 .31089 L .27292 .31123 L .27572 .31137 L .2771 .31143 L .27838 .31147 L .27951 .31151 L .28076 .31154 L .28202 .31156 L .28271 .31157 L .28335 .31158 L .28458 .31158 L .28528 .31159 L .28593 .31159 L .28724 .31158 L .28797 .31157 L .28864 .31156 L .28984 .31154 L .29114 .31151 L .29349 .31144 L .29625 .31132 L .29918 .31116 L .30442 .31078 L .30935 .31032 L .31385 .30981 L .32399 .30838 L .3423 .30481 L .36133 .29992 L .38207 .29342 L .42276 .278 L .46195 .26134 L Mistroke .50358 .24365 L .5437 .22837 L .5823 .21665 L .60228 .21206 L .61246 .21015 L .62336 .20844 L .63366 .20715 L .64303 .20625 L .64755 .20592 L .65246 .20562 L .6571 .2054 L .65919 .20533 L .66138 .20526 L .66254 .20524 L .66381 .20521 L .66497 .20519 L .66603 .20517 L .66728 .20516 L .66797 .20516 L .66862 .20515 L .66978 .20515 L .67103 .20515 L .67212 .20515 L .67332 .20516 L .67457 .20518 L .67574 .20519 L .67784 .20523 L .68008 .20529 L .68273 .20538 L .68562 .2055 L .69086 .20577 L .7007 .2065 L .71008 .20744 L .72045 .20875 L .74145 .21221 L .78162 .22141 L .82028 .2325 L .86138 .24534 L .90097 .25734 L .93905 .26737 L .97619 .27484 L Mfstroke 0 g [ .03 ] 0 setdash .03049 .61803 m .03053 .61718 L .03279 .58171 L .03527 .55188 L .0379 .52675 L .04262 .49192 L .04749 .46451 L .05205 .44384 L .06244 .408 L .07305 .38138 L .08274 .3625 L .09407 .34492 L .10458 .33172 L .12357 .31319 L .14429 .29837 L .16481 .28743 L .18342 .27979 L .20266 .27356 L .22348 .26827 L .24303 .26434 L .26449 .26092 L .30398 .25639 L .32349 .25476 L .3444 .25335 L .36421 .25227 L .38576 .25131 L .42561 .25001 L .44538 .24953 L .46639 .24911 L .50414 .24854 L .52349 .24832 L .54434 .24812 L .56399 .24797 L .58548 .24784 L .62511 .24765 L .64472 .24757 L .66567 .24751 L .68558 .24746 L .70716 .24742 L .74715 .24736 L .76702 .24733 L .78807 .24731 L .82595 .24728 L .8454 .24727 L .86629 .24726 L .88604 .24725 L .90757 .24725 L .94733 .24724 L .97619 .24723 L s 1 0 0 r [ .005 ] 0 setdash .02381 .37082 m .02499 .37082 L .02605 .37083 L .02729 .37085 L .02846 .37087 L .03053 .37092 L .03279 .371 L .03527 .37111 L .0379 .37125 L .04262 .37159 L .04749 .37205 L .05205 .37257 L .06244 .3741 L .07305 .37616 L .08274 .37851 L .10458 .38546 L .12357 .39349 L .14429 .40455 L .16561 .4187 L .18493 .43425 L .22406 .47499 L .26413 .53269 L .30268 .60821 L s .30268 .60821 m .30637 .61803 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{487, 300.875}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgc/eE[;`00?m?Cdol000200?ooc:ZZo`3Mool0okjn__o0b`00OemOGg20T?nI V@1;Rh/`0 00005P00104000Oo000005P00104000Oo00@/000<10040 3`4:00030@0100l12P000`40000?0@X000<100003`4:00080@000BL79`LD00030@0001T000<10000 3P0001H000<100006@000`40000E00051`0000406`000`40000I00030@00014000<100001@000`40 000I00030@0100h12`000`400@040@l00PL400030@0001T000<100006@000`40000I00030@000080 0`4D00030@0001T000<100006@000`40000500@740000`40000I00030@0000h0000F00030@000380 00<70000>0000`40000?00813P0:0C/000<79`L01P000`40001I00<14@000`40001100049`LW1bP0 00<100003P0001H000<10000<`000`L0001700812`050D<00PMX00<1EP041cD0000F00030@0003@0 00<70000@P040E80000000`L0000k00030@0004l00PMo00<1E`031bP0000F00030@0003T000P0001H0 00<10000DP020@h000D79`LW1`0Q00071bL79`LW1`3o0400000F00030@00054000<100004`0:1`l0 20Oo04L0000F00030@0002d000<100007`020B0000lW1bL79`LW1bL79`LW1bL0o`1?00005P000`40 000/00030@0001h00P7o0800000F00030@0002/000<100007P000`40003o0800000F00030@0002X0 00<100007@020Ol0P`0001H00P4Z00030@0001`00P7o08D0000F00030@0002L00P4M0081o`270000 5P000`40000V00030@0001/00P7o08T0000F00030@0002D000<100006P020Ol0R`0001H000<10000 90000`40000I0081o`2=00005P000`40000S00030@0001P00P7o08l0000F00030@00028000<10000 5`020Ol0T@0001H000<10000>P020Ol0T`0001H000<10000>0020Ol0U@0001H000<10000=P020Ol0 U`0001H000<10000=0020Ol0V@0001H000<10000@000`d0003o09<0000F00030@0000h000<10000 :P000`d0003o0940000F00030@0000h000<10000:`023Ol0T@0001H000<100003P000`40003o0;h0 000F00030@0000d000<10000;`000`d0003o08d0000F00813P000`40000`00033@000?l0S00001H0 00<100003@000`40003o0;l0000F00030@0000d000<10000`000`d0003o08<0000F00030@0000/000<10000?0023Ol0 P`0001H000<10000o`3?00005P000`40001=00033@000?l0O`0001H00P5?00033@000?l0OP0001H0 00<10000CP000`d0003o07h0000F00030@00050000<=0000o`1l00005P000`40001A00033@000?l0 N`0001H000<10000DP000`d0003o07X0000F00030@000?l0c`0001H000<10000D`000`d0003o07T0 000F00030@0005@00Pgo07T0000F00030@000?l0c`0001H000<10000E`000`d0003o07D0000F0003 0@0005P000<=0000o`1d00005P020@P000<10000CP000`d0003o07@0000F00030@0000L000<10000 o`3500005P000`40000700030@00050000<=0000o`1b00005P000`40000700030@00054000<=0000 o`1a00005P000`40000700030@000?l0a@0001H000<100001`000`40001C00033@000?l0K`0001H0 00<100001P000`40001E00033@000?l0KP0001H000<100001P000`40001E00033@000?l0KP0001H0 00<100001P000`40003o00000 5P001@40000107d000<=0000o`1=00005P001040005n00033@000?l0C@0001H000@10001O`000`d0 003o04`0000F00040@000Gl000<=0000o`1<00005P001040006000033@000?l0B`0000`00P480004 0@000H0000<=0000o`1;00002`001040004700040@000Ol0cP0000h000<100001@040H4000<=0000 o`1:000030020Ol0fP0000h000<10000o`3G00002`001040007o0=T0000<0081o`3J0000 \>"], ImageRangeCache->{{{0, 486}, {299.875, 0}} -> {-0.39662, -2.07738, 0.0178478, 0.0171895}}] }, Open ]], Cell[BoxData[{ \(\(J\_0\)\(\((x)\)\ \ \ --\)\ solid\ black\ line\), \(\(Y\_0\)\(\((x)\)\ \ \ --\)\ solid\ blue\ line\), \(\(K\_0\)\(\((x)\)\ \ \ --\)\ dashed\ line\), \(\(I\_0\)\(\((x)\)\ \ \ --\)\ red\ dotted\ line\)}], "Input", TextAlignment->Center] }, Open ]] }, Open ]] }, FrontEndVersion->"X 3.0", ScreenRectangle->{{0, 1152}, {0, 900}}, WindowSize->{590, 600}, WindowMargins->{{194, Automatic}, {Automatic, 96}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PaperSize"->{612, 792}, "PaperOrientation"->"Portrait", "Magnification"->1}, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of \ all cells in a given style. Make modifications to any definition using \ commands in the Format menu.\ \>", "Text"], Cell[CellGroupData[{ Cell["Style Environment Names", "Section"], Cell[StyleData[All, "Working"], PageWidth->WindowWidth, ScriptMinSize->9], Cell[StyleData[All, "Presentation"], PageWidth->WindowWidth, ScriptMinSize->12, FontSize->16], Cell[StyleData[All, "Condensed"], PageWidth->WindowWidth, CellBracketOptions->{"Margins"->{1, 1}, "Widths"->{0, 5}}, ScriptMinSize->8, FontSize->11], Cell[StyleData[All, "Printout"], PageWidth->PaperWidth, ScriptMinSize->5, FontSize->10, PrivateFontOptions->{"FontType"->"Outline"}] }, Closed]], Cell[CellGroupData[{ Cell["Notebook Options", "Section"], Cell["\<\ The options defined for the style below will be used at the \ Notebook level.\ \>", "Text"], Cell[StyleData["Notebook"], PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], None, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], None, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, StyleMenuListing->None] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headings", "Section"], Cell[CellGroupData[{ Cell[StyleData["Title"], CellMargins->{{12, Inherited}, {20, 40}}, CellGroupingRules->{"TitleGrouping", 0}, PageBreakBelow->False, CounterIncrements->"Title", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subtitle", 0}, {"Subsubtitle", 0}}, FontFamily->"Helvetica", FontSize->36, FontWeight->"Bold"], Cell[StyleData["Title", "Presentation"], CellMargins->{{24, 10}, {20, 40}}, LineSpacing->{1, 0}, FontSize->44], Cell[StyleData["Title", "Condensed"], CellMargins->{{8, 10}, {4, 8}}, FontSize->20], Cell[StyleData["Title", "Printout"], CellMargins->{{2, 10}, {15, 30}}, FontSize->24] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], CellMargins->{{12, Inherited}, {10, 15}}, CellGroupingRules->{"TitleGrouping", 10}, PageBreakBelow->False, CounterIncrements->"Subtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subsubtitle", 0}}, FontFamily->"Helvetica", FontSize->24], Cell[StyleData["Subtitle", "Presentation"], CellMargins->{{24, 10}, {15, 20}}, LineSpacing->{1, 0}, FontSize->36], Cell[StyleData["Subtitle", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, FontSize->14], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{2, 10}, {10, 15}}, FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubtitle"], CellMargins->{{12, Inherited}, {10, 20}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontFamily->"Helvetica", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Subsubtitle", "Presentation"], CellMargins->{{24, 10}, {10, 20}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Subsubtitle", "Condensed"], CellMargins->{{8, 10}, {8, 12}}, FontSize->12], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{2, 10}, {8, 10}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellFrame->{{0, 0}, {0, 3}}, CellDingbat->"\[FilledDiamond]", CellMargins->{{25, Inherited}, {8, 24}}, CellGroupingRules->{"SectionGrouping", 30}, PageBreakBelow->False, CellFrameLabelMargins->6, TextAlignment->Center, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->24, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Section", "Presentation"], CellFrame->{{0, 0}, {0, 3}}, CellDingbat->"\[FilledDiamond]", CellMargins->{{40, 10}, {11, 32}}, TextAlignment->Center, LineSpacing->{1, 0}, FontSize->24, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Section", "Condensed"], CellFrame->{{0, 0}, {0, 3}}, CellDingbat->"\[FilledDiamond]", CellMargins->{{18, Inherited}, {6, 12}}, TextAlignment->Center, FontSize->24, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Section", "Printout"], CellFrame->{{0, 0}, {0, 3}}, CellDingbat->"\[FilledDiamond]", CellMargins->{{13, 0}, {7, 22}}, TextAlignment->Center, FontSize->24, FontColor->RGBColor[0, 0, 1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{22, Inherited}, {8, 20}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CellFrameLabelMargins->6, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Times", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{22, Inherited}, {8, 18}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, CellFrameLabelMargins->6, CounterIncrements->"Subsubsection", FontFamily->"Times", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontSize->11] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{12, 10}, {7, 7}}, LineSpacing->{1, 3}, CounterIncrements->"Text", FontFamily->"Times"], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{12, 10}, {6, 6}}, LineSpacing->{1, 3}, CounterIncrements->"SmallText", FontFamily->"Helvetica", FontSize->9], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{45, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{47, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Output"], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageSize->{175, 175}, ImageMargins->{{38, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Printout"], ImageSize->{250, 250}, ImageMargins->{{30, Inherited}, {Inherited, 0}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Automatic Numbering", "Section"], Cell["\<\ The following styles are useful for numbered equations, figures, \ etc. They automatically give the cell a FrameLabel containing a reference to \ a particular counter, and also increment that counter.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["NumberedEquation"], CellFrameLabels->{{None, Cell[ TextData[ {"(", CounterBox[ "NumberedEquation"], ")"}]]}, {None, None}}, DefaultFormatType->DefaultInputFormatType, TextAlignment->Center, CounterIncrements->"NumberedEquation", FormatTypeAutoConvert->False], Cell[StyleData["NumberedEquation", "Presentation"]], Cell[StyleData["NumberedEquation", "Condensed"]], Cell[StyleData["NumberedEquation", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NumberedFigure"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Figure ", CounterBox[ "NumberedFigure"]}]], None}}, CounterIncrements->"NumberedFigure", ImageMargins->{{43, Inherited}, {Inherited, 0}}, FormatTypeAutoConvert->False], Cell[StyleData["NumberedFigure", "Presentation"]], Cell[StyleData["NumberedFigure", "Condensed"]], Cell[StyleData["NumberedFigure", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NumberedTable"], CellMargins->{{44, Inherited}, {Inherited, Inherited}}, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Table ", CounterBox[ "NumberedTable"]}]], None}}, TextAlignment->Center, CounterIncrements->"NumberedTable", FormatTypeAutoConvert->False], Cell[StyleData["NumberedTable", "Presentation"]], Cell[StyleData["NumberedTable", "Condensed"]], Cell[StyleData["NumberedTable", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], ShowCellBracket->False, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ScriptLevel->1, SingleLetterItalics->True, StyleMenuListing->None, GridBoxOptions->{ColumnWidths->Automatic}], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{0, 0}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ChemicalFormula"], ShowCellBracket->False, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, AutoSpacing->False, ScriptLevel->1, ScriptBaselineShifts->{0.6, Automatic}, SingleLetterItalics->True, ZeroWidthTimes->True, GridBoxOptions->{ColumnWidths->Automatic}], Cell[StyleData["ChemicalFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["ChemicalFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["ChemicalFormula", "Printout"], CellMargins->{{0, 0}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], ShowCellBracket->False, CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, ScriptLevel->0, SingleLetterItalics->True, StyleMenuListing->None, UnderoverscriptBoxOptions->{LimitsPositioning->True}, GridBoxOptions->{ColumnWidths->Automatic}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}], Cell[StyleData["DisplayFormula", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], ShowCellBracket->False, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->15], Cell[StyleData["Program", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->10.5], Cell[StyleData["Program", "Printout"], CellMargins->{{0, 0}, {6, 6}}, FontSize->9.5] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10, FontWeight->"Bold"] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Times", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Times", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Times", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder \ objects in palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->True, StyleMenuListing->None], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SelectionPlaceholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->Primary, StyleMenuListing->None, DrawHighlighted->True], Cell[StyleData["SelectionPlaceholder", "Presentation"]], Cell[StyleData["SelectionPlaceholder", "Condensed"]], Cell[StyleData["SelectionPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles \ of most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, FontColor->GrayLevel[0]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{1, -5}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an \ inline cell within another.\ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]] }, Open ]] }] ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{ "primes"->{ Cell[2818, 92, 1964, 39, 548, "Output", CellTags->"primes"]}, "Si"->{ Cell[7579, 231, 128, 4, 55, "Input", CellTags->"Si"]}, "Gamma"->{ Cell[7941, 248, 87, 1, 101, "Section", CellTags->"Gamma"]}, "Err"->{ Cell[46657, 1329, 85, 1, 101, "Section", CellTags->"Err"]} } *) (*CellTagsIndex CellTagsIndex->{ {"primes", 95440, 3027}, {"Si", 95522, 3030}, {"Gamma", 95600, 3033}, {"Err", 95681, 3036} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1731, 51, 221, 8, 150, "Title"], Cell[1955, 61, 124, 3, 70, "Subtitle"], Cell[2082, 66, 533, 14, 224, "Text"], Cell[CellGroupData[{ Cell[2640, 84, 52, 0, 72, "Section"], Cell[CellGroupData[{ Cell[2717, 88, 98, 2, 27, "Input"], Cell[2818, 92, 1964, 39, 548, "Output", CellTags->"primes"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[4831, 137, 59, 0, 72, "Section"], Cell[4893, 139, 815, 24, 154, "Output"], Cell[CellGroupData[{ Cell[5733, 167, 168, 3, 27, "Input"], Cell[5904, 172, 403, 8, 56, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[6356, 186, 65, 0, 101, "Section"], Cell[6424, 188, 209, 6, 89, "Input"], Cell[6636, 196, 173, 5, 83, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[6846, 206, 72, 0, 101, "Section"], Cell[CellGroupData[{ Cell[6943, 210, 151, 3, 59, "Input"], Cell[7097, 215, 445, 11, 85, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7579, 231, 128, 4, 55, "Input", CellTags->"Si"], Cell[7710, 237, 182, 5, 85, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[7941, 248, 87, 1, 101, "Section", CellTags->"Gamma"], Cell[8031, 251, 140, 3, 59, "Input"], Cell[8174, 256, 507, 13, 85, "Input"], Cell[CellGroupData[{ Cell[8706, 273, 314, 5, 59, "Input"], Cell[9023, 280, 37585, 1043, 306, 11180, 712, "GraphicsData", "PostScript", "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[46657, 1329, 85, 1, 101, "Section", CellTags->"Err"], Cell[CellGroupData[{ Cell[46767, 1334, 166, 5, 71, "Input"], Cell[46936, 1341, 114, 4, 47, "Output"] }, Open ]], Cell[47065, 1348, 169, 4, 71, "Input"], Cell[47237, 1354, 151, 4, 92, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[47425, 1363, 63, 0, 72, "Section"], Cell[47491, 1365, 137, 3, 27, "Input"], Cell[CellGroupData[{ Cell[47653, 1372, 74, 2, 32, "Input"], Cell[47730, 1376, 286, 9, 77, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[48053, 1390, 298, 6, 59, "Input"], Cell[48354, 1398, 19097, 622, 309, 6876, 467, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[67466, 2023, 273, 5, 75, "Input"] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)