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- 16\/9\ \((\(-4\) + z)\)\^4 - 1\/252\ \((\(-4\) + z)\)\^7 - \(512\ z\)\/9 - 32\/3\ \((\(-4\) + z)\)\^2\ z + 2\/3\ \((\(-4\) + z)\)\^4\ z + 1\/72\ \((\(-4\) + z)\)\^6\ z - 256\/15\ \((16 - 4\ z - z\^2)\) + 1\/60\ \((\(-4\) + z)\)\^5\ \((16 - 4\ z - z\^2)\) - 16\/9\ z\ \((\(-96\) + 24\ z + z\^2)\) + 1\/144\ \((\(-4\) + z)\)\^4\ z\ \((\(-96\) + 24\ z + z\^2)\) - 64\/9\ \((\(-64\) + 32\ z - z\^3)\) + 1\/9\ \((\(-4\) + z)\)\^3\ \((\(-64\) + 32\ z - z\^3)\))\)\ UnitStep[\(-8\) + z] + \((\(-\(2653\/9\)\) - 2048\/9\ \((\(-1\) - z)\) - \(81\ \((1 - z)\)\)\/2 - 9\ \((\(-4\) + z)\)\^3 + 3\ \((\(-4\) + z)\)\^4 + 1\/18\ \((1 - z)\)\ \((\(-4\) + z)\)\^6 + 1\/63\ \((\(-4\) + z)\)\^7 - 256\/9\ \((\(-3\) + z)\)\^3 + 64\/9\ \((\(-3\) + z)\)\^4 + 1\/18\ \((\(-1\) - z)\)\ \((\(-3\) + z)\)\^6 + 1\/63\ \((\(-3\) + z)\)\^7 + 27\/2\ \((\(-4\) + z)\)\^2\ \((\(-1\) + z)\) - 3\/2\ \((\(-4\) + z)\)\^4\ \((\(-1\) + z)\) + 128\/3\ \((\(-3\) + z)\)\^2\ \((1 + z)\) - 8\/3\ \((\(-3\) + z)\)\^4\ \((1 + z)\) - 81\/5\ \((\(-11\) + z + z\^2)\) + 1\/15\ \((\(-4\) + z)\)\^5\ \((\(-11\) + z + z\^2)\) - 1024\/15\ \((\(-11\) + 6\ z + z\^2)\) + 1\/15\ \((\(-3\) + z)\)\^5\ \((\(-11\) + 6\ z + z\^2)\) - 64\/9\ \((71 + 45\ z - 27\ z\^2 - z\^3)\) + 1\/36\ \((\(-3\) + z)\)\^4\ \((71 + 45\ z - 27\ z\^2 - z\^3)\) - 9\/4\ \((\(-71\) + 87\ z - 15\ z\^2 - z\^3)\) + 1\/36\ \((\(-4\) + z)\)\^4\ \((\(-71\) + 87\ z - 15\ z\^2 - z\^3)\) - 9\ \((44 - 15\ z - 3\ z\^2 + z\^3)\) + 1\/3\ \((\(-4\) + z)\)\^3\ \((44 - 15\ z - 3\ z\^2 + z\^3)\) - 256\/9\ \((33 - 29\ z + 3\ z\^2 + z\^3)\) + 4\/9\ \((\(-3\) + z)\)\^3\ \((33 - 29\ z + 3\ z\^2 + z\^3)\))\)\ UnitStep[\(-7\) + z] + \((532 + 8\/3\ \((\(-4\) + z)\)\^3 - 4\/3\ \((\(-4\) + z)\)\^4 - 1\/42\ \((\(-4\) + z)\)\^7 + 36\ \((\(-3\) + z)\)\^3 - 12\ \((\(-3\) + z)\)\^4 - 4\/63\ \((\(-3\) + z)\)\^7 - 16\/3\ \((\(-2\) + z)\) - 4\ \((\(-4\) + z)\)\^2\ \((\(-2\) + z)\) + \((\(-4\) + z)\)\^4\ \((\(-2\) + z)\) + 1\/12\ \((\(-4\) + z)\)\^6\ \((\(-2\) + z)\) + 128\/3\ \((\(-2\) + z)\)\^3 - 32\/3\ \((\(-2\) + z)\)\^4 - 1\/42\ \((\(-2\) + z)\)\^7 - 162\ z - 54\ \((\(-3\) + z)\)\^2\ z + 6\ \((\(-3\) + z)\)\^4\ z + 2\/9\ \((\(-3\) + z)\)\^6\ z - \(1024\ \((2 + z)\)\)\/3 - 64\ \((\(-2\) + z)\)\^2\ \((2 + z)\) + 4\ \((\(-2\) + z)\)\^4\ \((2 + z)\) + 1\/12\ \((\(-2\) + z)\)\^6\ \((2 + z)\) - 512\/5\ \((4 - 8\ z - z\^2)\) + 1\/10\ \((\(-2\) + z)\)\^5\ \((4 - 8\ z - z\^2)\) - 16\/5\ \((4 + 2\ z - z\^2)\) + 1\/10\ \((\(-4\) + z)\)\^5\ \((4 + 2\ z - z\^2)\) + 324\/5\ \((\(-9\) + 3\ z + z\^2)\) - 4\/15\ \((\(-3\) + z)\)\^5\ \((\(-9\) + 3\ z + z\^2)\) - 9\ z\ \((\(-54\) + 18\ z + z\^2)\) + 1\/9\ \((\(-3\) + z)\)\^4\ z\ \((\(-54\) + 18\ z + z\^2)\) - 8\/3\ \((\(-16\) - 4\ z + 6\ z\^2 - z\^3)\) + 1\/3\ \((\(-4\) + z)\)\^3\ \((\(-16\) - 4\ z + 6\ z\^2 - z\^3)\) + 36\ \((27 - 18\ z + z\^3)\) - 4\/3\ \((\(-3\) + z)\)\^3\ \((27 - 18\ z + z\^3)\) - 2\/3\ \((88 - 60\ z + 6\ z\^2 + z\^3)\) + 1\/24\ \((\(-4\) + z)\)\^4\ \((88 - 60\ z + 6\ z\^2 + z\^3)\) + 128\/3\ \((8 - 20\ z + 6\ z\^2 + z\^3)\) - 2\/3\ \((\(-2\) + z)\)\^3\ \((8 - 20\ z + 6\ z\^2 + z\^3)\) - 32\/3\ \((\(-88\) + 12\ z + 30\ z\^2 + z\^3)\) + 1\/24\ \((\(-2\) + z)\)\^4\ \((\(-88\) + 12\ z + 30\ z\^2 + z\^3)\))\)\ UnitStep[\(-6\) + z] + \((\(-\(4325\/9\)\) - 2048\/9\ \((\(-3\) - z)\) - 243\ \((\(-1\) - z)\) - \(64\ \((1 - z)\)\)\/3 - 1\/9\ \((\(-4\) + z)\)\^3 + 1\/9\ \((\(-4\) + z)\)\^4 + 1\/18\ \((3 - z)\)\ \((\(-4\) + z)\)\^6 + 1\/63\ \((\(-4\) + z)\)\^7 + 1\/18\ \((\(-3\) + z)\) + 1\/6\ \((\(-4\) + z)\)\^2\ \((\(-3\) + z)\) - 1\/6\ \((\(-4\) + z)\)\^4\ \((\(-3\) + z)\) - 32\/3\ \((\(-3\) + z)\)\^3 + 16\/3\ \((\(-3\) + z)\)\^4 + 1\/3\ \((1 - z)\)\ \((\(-3\) + z)\)\^6 + 2\/21\ \((\(-3\) + z)\)\^7 - 54\ \((\(-2\) + z)\)\^3 + 18\ \((\(-2\) + z)\)\^4 + 1\/3\ \((\(-1\) - z)\)\ \((\(-2\) + z)\)\^6 + 2\/21\ \((\(-2\) + z)\)\^7 + 16\ \((\(-3\) + z)\)\^2\ \((\(-1\) + z)\) - 4\ \((\(-3\) + z)\)\^4\ \((\(-1\) + z)\) - 256\/9\ \((\(-1\) + z)\)\^3 + 64\/9\ \((\(-1\) + z)\)\^4 + 1\/18\ \((\(-3\) - z)\)\ \((\(-1\) + z)\)\^6 + 1\/63\ \((\(-1\) + z)\)\^7 + 81\ \((\(-2\) + z)\)\^2\ \((1 + z)\) - 9\ \((\(-2\) + z)\)\^4\ \((1 + z)\) + 128\/3\ \((\(-1\) + z)\)\^2\ \((3 + z)\) - 8\/3\ \((\(-1\) + z)\)\^4\ \((3 + z)\) + 1\/15\ \((\(-5\) + 5\ z - z\^2)\) - 64\/5\ \((\(-5\) + z\^2)\) + 2\/5\ \((\(-3\) + z)\)\^5\ \((\(-5\) + z\^2)\) + 1\/15\ \((\(-4\) + z)\)\^5\ \((5 - 5\ z + z\^2)\) - 486\/5\ \((\(-5\) + 5\ z + z\^2)\) + 2\/5\ \((\(-2\) + z)\)\^5\ \((\(-5\) + 5\ z + z\^2)\) - 1024\/15\ \((5 + 10\ z + z\^2)\) + 1\/15\ \((\(-1\) + z)\)\^5\ \((5 + 10\ z + z\^2)\) - 64\/9\ \((45 - 75\ z - 33\ z\^2 - z\^3)\) + 1\/36\ \((\(-1\) + z)\)\^4\ \((45 - 75\ z - 33\ z\^2 - z\^3)\) - 27\/2\ \((35 + 15\ z - 21\ z\^2 - z\^3)\) + 1\/6\ \((\(-2\) + z)\)\^4\ \((35 + 15\ z - 21\ z\^2 - z\^3)\) - 8\/3\ \((\(-35\) + 45\ z - 9\ z\^2 - z\^3)\) + 1\/6\ \((\(-3\) + z)\)\^4\ \((\(-35\) + 45\ z - 9\ z\^2 - z\^3)\) + 1\/36\ \((\(-4\) + z)\)\^4\ \((\(-45\) + 15\ z + 3\ z\^2 - z\^3)\) + 1\/9\ \((20 - 25\ z + 9\ z\^2 - z\^3)\) + 1\/9\ \((\(-4\) + z)\)\^3\ \((\(-20\) + 25\ z - 9\ z\^2 + z\^3)\) + 1\/36\ \((45 - 15\ z - 3\ z\^2 + z\^3)\) - 32\/3\ \((15 - 5\ z - 3\ z\^2 + z\^3)\) + 4\/3\ \((\(-3\) + z)\)\^3\ \((15 - 5\ z - 3\ z\^2 + z\^3)\) - 54\ \((10 - 15\ z + 3\ z\^2 + z\^3)\) + 2\ \((\(-2\) + z)\)\^3\ \((10 - 15\ z + 3\ z\^2 + z\^3)\) - 256\/9\ \((\(-5\) - 5\ z + 9\ z\^2 + z\^3)\) + 4\/9\ \((\(-1\) + z)\)\^3\ \((\(-5\) - 5\ z + 9\ z\^2 + z\^3)\)) \)\ UnitStep[\(-5\) + z] + \((9904\/63 + \((\(-4\) + z)\)\^7\/5040 + 4\/9\ \((\(-3\) + z)\)\^3 - 4\/9\ \((\(-3\) + z)\)\^4 - 4\/63\ \((\(-3\) + z)\)\^7 - 2\/9\ \((\(-2\) + z)\) - 2\/3\ \((\(-3\) + z)\)\^2\ \((\(-2\) + z)\) + 2\/3\ \((\(-3\) + z)\)\^4\ \((\(-2\) + z)\) + 2\/9\ \((\(-3\) + z)\)\^6\ \((\(-2\) + z)\) + 16\ \((\(-2\) + z)\)\^3 - 8\ \((\(-2\) + z)\)\^4 - 1\/7\ \((\(-2\) + z)\)\^7 + 36\ \((\(-1\) + z)\)\^3 - 12\ \((\(-1\) + z)\)\^4 - 4\/63\ \((\(-1\) + z)\)\^7 - 32\ z - 24\ \((\(-2\) + z)\)\^2\ z + 6\ \((\(-2\) + z)\)\^4\ z + 1\/2\ \((\(-2\) + z)\)\^6\ z - 162\ \((2 + z)\) - 54\ \((\(-1\) + z)\)\^2\ \((2 + z)\) + 6\ \((\(-1\) + z)\)\^4\ \((2 + z)\) + 2\/9\ \((\(-1\) + z)\)\^6\ \((2 + z)\) + 4\/15\ \((1 - 3\ z + z\^2)\) - 4\/15\ \((\(-3\) + z)\)\^5\ \((1 - 3\ z + z\^2)\) + 96\/5\ \((\(-4\) + 2\ z + z\^2)\) - 3\/5\ \((\(-2\) + z)\)\^5\ \((\(-4\) + 2\ z + z\^2)\) + 324\/5\ \((1 + 7\ z + z\^2)\) - 4\/15\ \((\(-1\) + z)\)\^5\ \((1 + 7\ z + z\^2)\) - 4\ z\ \((\(-24\) + 12\ z + z\^2)\) + 1\/4\ \((\(-2\) + z)\)\^4\ z\ \((\(-24\) + 12\ z + z\^2)\) + 1\/9\ \((\(-28\) + 18\ z - z\^3)\) + 1\/9\ \((\(-3\) + z)\)\^4\ \((28 - 18\ z + z\^3)\) + 16\ \((8 - 8\ z + z\^3)\) - 2\ \((\(-2\) + z)\)\^3\ \((8 - 8\ z + z\^3)\) + 4\/9\ \((\(-3\) + 10\ z - 6\ z\^2 + z\^3)\) - 4\/9\ \((\(-3\) + z)\)\^3\ \((\(-3\) + 10\ z - 6\ z\^2 + z\^3)\) + 36\ \((\(-1\) - 6\ z + 6\ z\^2 + z\^3)\) - 4\/3\ \((\(-1\) + z)\)\^3\ \((\(-1\) - 6\ z + 6\ z\^2 + z\^3)\) - 9\ \((\(-28\) + 30\ z + 24\ z\^2 + z\^3)\) + 1\/9\ \((\(-1\) + z)\)\^4\ \((\(-28\) + 30\ z + 24\ z\^2 + z\^3)\) + 1\/6\ \(( 8192\/21 + \(128\ z\^3\)\/3 - \(32\ z\^4\)\/3 - z\^7\/42 - \(1024\ \((4 + z)\)\)\/3 - 64\ z\^2\ \((4 + z)\) + 4\ z\^4\ \((4 + z)\) + 1\/12\ z\^6\ \((4 + z)\) - 512\/5\ \((\(-16\) - 12\ z - z\^2)\) + 1\/10\ z\^5\ \((\(-16\) - 12\ z - z\^2)\) + 128\/3\ z\ \((16 + 12\ z + z\^2)\) - 2\/3\ z\^4\ \((16 + 12\ z + z\^2)\) - 32\/3\ \((64 + 144\ z + 36\ z\^2 + z\^3)\) + 1\/24\ z\^4\ \((64 + 144\ z + 36\ z\^2 + z\^3)\))\))\)\ UnitStep[\(-4\) + z] + \((\(-\(86\/7\)\) + 1\/6\ \(( 1\/3\ \((3 - z)\)\ \((\(-3\) + z)\)\^6 + 23\/70\ \((\(-3\) + z)\)\^7)\) - 64\/3\ \((\(-1\) - z)\) - 2\/3\ \((\(-2\) + z)\)\^3 + 2\/3\ \((\(-2\) + z)\)\^4 + 1\/3\ \((1 - z)\)\ \((\(-2\) + z)\)\^6 + 2\/21\ \((\(-2\) + z)\)\^7 + 1\/3\ \((\(-1\) + z)\) + \((\(-2\) + z)\)\^2\ \((\(-1\) + z)\) - \((\(-2\) + z)\)\^4\ \((\(-1\) + z)\) - 32\/3\ \((\(-1\) + z)\)\^3 + 16\/3\ \((\(-1\) + z)\)\^4 + 1\/3\ \((\(-1\) - z)\)\ \((\(-1\) + z)\)\^6 + 2\/21\ \((\(-1\) + z)\)\^7 + 16\ \((\(-1\) + z)\)\^2\ \((1 + z)\) - 4\ \((\(-1\) + z)\)\^4\ \((1 + z)\) - 2\/5\ \((\(-1\) - z + z\^2)\) + 2\/5\ \((\(-2\) + z)\)\^5\ \((\(-1\) - z + z\^2)\) - 64\/5\ \((\(-1\) + 4\ z + z\^2)\) + 2\/5\ \((\(-1\) + z)\)\^5\ \((\(-1\) + 4\ z + z\^2)\) - 8\/3\ \((11 - 3\ z - 15\ z\^2 - z\^3)\) + 1\/6\ \((\(-1\) + z)\)\^4\ \((11 - 3\ z - 15\ z\^2 - z\^3)\) + 1\/6\ \((\(-2\) + z)\)\^4\ \((\(-11\) + 15\ z - 3\ z\^2 - z\^3)\) - 2\/3\ \((2 + z - 3\ z\^2 + z\^3)\) + 2\/3\ \((\(-2\) + z)\)\^3\ \((2 + z - 3\ z\^2 + z\^3)\) + 1\/6\ \((11 - 15\ z + 3\ z\^2 + z\^3)\) - 32\/3\ \((1 - 5\ z + 3\ z\^2 + z\^3)\) + 4\/3\ \((\(-1\) + z)\)\^3\ \((1 - 5\ z + 3\ z\^2 + z\^3)\) + 1\/6\ \(( \(-\(1458\/7\)\) - 243\ \((\(-3\) - z)\) - 54\ z\^3 + 18\ z\^4 + 1\/3\ \((\(-3\) - z)\)\ z\^6 + \(2\ z\^7\)\/21 + 81\ z\^2\ \((3 + z)\) - 9\ z\^4\ \((3 + z)\) - 486\/5\ \((9 + 9\ z + z\^2)\) - 54\ z\ \((9 + 9\ z + z\^2)\) + 2\ z\^4\ \((9 + 9\ z + z\^2)\) + 2\/5\ z\^5\ \((9 + 9\ z + z\^2)\) - 27\/2\ \((\(-27\) - 81\ z - 27\ z\^2 - z\^3)\) + 1\/6\ z\^4\ \((\(-27\) - 81\ z - 27\ z\^2 - z\^3)\))\))\)\ UnitStep[\(-3\) + z] + \((4\/63 + 1\/840\ \((\(-2\) + z)\)\^7 + 4\/9\ \((\(-1\) + z)\)\^3 - 4\/9\ \((\(-1\) + z)\)\^4 - 4\/63\ \((\(-1\) + z)\)\^7 - \(2\ z\)\/9 - 2\/3\ \((\(-1\) + z)\)\^2\ z + 2\/3\ \((\(-1\) + z)\)\^4\ z + 2\/9\ \((\(-1\) + z)\)\^6\ z + 4\/15\ \((\(-1\) + z + z\^2)\) - 4\/15\ \((\(-1\) + z)\)\^5\ \((\(-1\) + z + z\^2)\) - 1\/9\ z\ \((\(-6\) + 6\ z + z\^2)\) + 1\/9\ \((\(-1\) + z)\)\^4\ z\ \((\(-6\) + 6\ z + z\^2)\) + 4\/9\ \((1 - 2\ z + z\^3)\) - 4\/9\ \((\(-1\) + z)\)\^3\ \((1 - 2\ z + z\^3)\) + 1\/6\ \(( 128\/7 + 16\ z\^3 - 8\ z\^4 - z\^7\/7 - 32\ \((2 + z)\) - 24\ z\^2\ \((2 + z)\) + 6\ z\^4\ \((2 + z)\) + 1\/2\ z\^6\ \((2 + z)\) + 96\/5\ \((4 + 6\ z + z\^2)\) + 16\ z\ \((4 + 6\ z + z\^2)\) - 2\ z\^4\ \((4 + 6\ z + z\^2)\) - 3\/5\ z\^5\ \((4 + 6\ z + z\^2)\) - 4\ \((8 + 36\ z + 18\ z\^2 + z\^3)\) + 1\/4\ z\^4\ \((8 + 36\ z + 18\ z\^2 + z\^3)\))\))\)\ UnitStep[\(-2\) + z] + \((1\/6\ \(( 1\/3\ \((1 - z)\)\ \((\(-1\) + z)\)\^6 + 23\/70\ \((\(-1\) + z)\)\^7)\) + 1\/6\ \(( \(-\(2\/21\)\) - \(2\ z\^3\)\/3 + \(2\ z\^4\)\/3 + 1\/3\ \((\(-1\) - z)\)\ z\^6 + \(2\ z\^7\)\/21 + \(1 + z\)\/3 + z\^2\ \((1 + z)\) - z\^4\ \((1 + z)\) - 2\/5\ \((1 + 3\ z + z\^2)\) - 2\/3\ z\ \((1 + 3\ z + z\^2)\) + 2\/3\ z\^4\ \((1 + 3\ z + z\^2)\) + 2\/5\ z\^5\ \((1 + 3\ z + z\^2)\) + 1\/6\ z\^4\ \((\(-1\) - 9\ z - 9\ z\^2 - z\^3)\) + 1\/6\ \((1 + 9\ z + 9\ z\^2 + z\^3)\))\))\)\ UnitStep[\(-1\) + z] + \(z\^7\ UnitStep[z]\)\/5040\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[%]\)], "Input"], Cell[BoxData[ \(\(1\/5040\(( \((\(-8\) + z)\)\^7\ UnitStep[\(-8\) + z] - 8\ \((\(-7\) + z)\)\^7\ UnitStep[\(-7\) + z] - 7838208\ UnitStep[\(-6\) + z] + 9144576\ z\ UnitStep[\(-6\) + z] - 4572288\ z\^2\ UnitStep[\(-6\) + z] + 1270080\ z\^3\ UnitStep[\(-6\) + z] - 211680\ z\^4\ UnitStep[\(-6\) + z] + 21168\ z\^5\ UnitStep[\(-6\) + z] - 1176\ z\^6\ UnitStep[\(-6\) + z] + 28\ z\^7\ UnitStep[\(-6\) + z] + 4375000\ UnitStep[\(-5\) + z] - 6125000\ z\ UnitStep[\(-5\) + z] + 3675000\ z\^2\ UnitStep[\(-5\) + z] - 1225000\ z\^3\ UnitStep[\(-5\) + z] + 245000\ z\^4\ UnitStep[\(-5\) + z] - 29400\ z\^5\ UnitStep[\(-5\) + z] + 1960\ z\^6\ UnitStep[\(-5\) + z] - 56\ z\^7\ UnitStep[\(-5\) + z] - 1146880\ UnitStep[\(-4\) + z] + 2007040\ z\ UnitStep[\(-4\) + z] - 1505280\ z\^2\ UnitStep[\(-4\) + z] + 627200\ z\^3\ UnitStep[\(-4\) + z] - 156800\ z\^4\ UnitStep[\(-4\) + z] + 23520\ z\^5\ UnitStep[\(-4\) + z] - 1960\ z\^6\ UnitStep[\(-4\) + z] + 70\ z\^7\ UnitStep[\(-4\) + z] + 122472\ UnitStep[\(-3\) + z] - 285768\ z\ UnitStep[\(-3\) + z] + 285768\ z\^2\ UnitStep[\(-3\) + z] - 158760\ z\^3\ UnitStep[\(-3\) + z] + 52920\ z\^4\ UnitStep[\(-3\) + z] - 10584\ z\^5\ UnitStep[\(-3\) + z] + 1176\ z\^6\ UnitStep[\(-3\) + z] - 56\ z\^7\ UnitStep[\(-3\) + z] - 3584\ UnitStep[\(-2\) + z] + 12544\ z\ UnitStep[\(-2\) + z] - 18816\ z\^2\ UnitStep[\(-2\) + z] + 15680\ z\^3\ UnitStep[\(-2\) + z] - 7840\ z\^4\ UnitStep[\(-2\) + z] + 2352\ z\^5\ UnitStep[\(-2\) + z] - 392\ z\^6\ UnitStep[\(-2\) + z] + 28\ z\^7\ UnitStep[\(-2\) + z] + 8\ UnitStep[\(-1\) + z] - 56\ z\ UnitStep[\(-1\) + z] + 168\ z\^2\ UnitStep[\(-1\) + z] - 280\ z\^3\ UnitStep[\(-1\) + z] + 280\ z\^4\ UnitStep[\(-1\) + z] - 168\ z\^5\ UnitStep[\(-1\) + z] + 56\ z\^6\ UnitStep[\(-1\) + z] - 8\ z\^7\ UnitStep[\(-1\) + z] + z\^7\ UnitStep[z])\)\)\)], "Output"] }, Closed]], Cell[BoxData[ \(g8fun[z_] := \(1\/5040\) \((\((\(-8\) + z)\)\^7\ UnitStep[\(-8\) + z] - 8\ \((\(-7\) + z)\)\^7\ UnitStep[\(-7\) + z] - 7838208\ UnitStep[\(-6\) + z] + 9144576\ z\ UnitStep[\(-6\) + z] - 4572288\ z\^2\ UnitStep[\(-6\) + z] + 1270080\ z\^3\ UnitStep[\(-6\) + z] - 211680\ z\^4\ UnitStep[\(-6\) + z] + 21168\ z\^5\ UnitStep[\(-6\) + z] - 1176\ z\^6\ UnitStep[\(-6\) + z] + 28\ z\^7\ UnitStep[\(-6\) + z] + 4375000\ UnitStep[\(-5\) + z] - 6125000\ z\ UnitStep[\(-5\) + z] + 3675000\ z\^2\ UnitStep[\(-5\) + z] - 1225000\ z\^3\ UnitStep[\(-5\) + z] + 245000\ z\^4\ UnitStep[\(-5\) + z] - 29400\ z\^5\ UnitStep[\(-5\) + z] + 1960\ z\^6\ UnitStep[\(-5\) + z] - 56\ z\^7\ UnitStep[\(-5\) + z] - 1146880\ UnitStep[\(-4\) + z] + 2007040\ z\ UnitStep[\(-4\) + z] - 1505280\ z\^2\ UnitStep[\(-4\) + z] + 627200\ z\^3\ UnitStep[\(-4\) + z] - 156800\ z\^4\ UnitStep[\(-4\) + z] + 23520\ z\^5\ UnitStep[\(-4\) + z] - 1960\ z\^6\ UnitStep[\(-4\) + z] + 70\ z\^7\ UnitStep[\(-4\) + z] + 122472\ UnitStep[\(-3\) + z] - 285768\ z\ UnitStep[\(-3\) + z] + 285768\ z\^2\ UnitStep[\(-3\) + z] - 158760\ z\^3\ UnitStep[\(-3\) + z] + 52920\ z\^4\ UnitStep[\(-3\) + z] - 10584\ z\^5\ UnitStep[\(-3\) + z] + 1176\ z\^6\ UnitStep[\(-3\) + z] - 56\ z\^7\ UnitStep[\(-3\) + z] - 3584\ UnitStep[\(-2\) + z] + 12544\ z\ UnitStep[\(-2\) + z] - 18816\ z\^2\ UnitStep[\(-2\) + z] + 15680\ z\^3\ UnitStep[\(-2\) + z] - 7840\ z\^4\ UnitStep[\(-2\) + z] + 2352\ z\^5\ UnitStep[\(-2\) + z] - 392\ z\^6\ UnitStep[\(-2\) + z] + 28\ z\^7\ UnitStep[\(-2\) + z] + 8\ UnitStep[\(-1\) + z] - 56\ z\ UnitStep[\(-1\) + z] + 168\ z\^2\ 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