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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a9t5.01

 Input Form

 Hypergeometric2F1[-(19/4), 19/4, 4, z] == (1/(140821065 Pi Sqrt[1 + Sqrt[z]] z^3)) (256 ((-608 - 608 Sqrt[z] - 4237 z - 4237 z^(3/2) - 39102 z^2 - 39102 z^(5/2) + 940515 z^3 + 940515 z^(7/2) - 3407304 z^4 - 3407304 z^(9/2) + 5018832 z^5 + 5018832 z^(11/2) - 3357120 z^6 - 3357120 z^(13/2) + 848640 z^7 + 848640 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (-608 - 4085 z - 38000 z^2 - 149553 z^3 + 2772390 z^4 - 8664144 z^5 + 11525280 z^6 - 7138560 z^7 + 1697280 z^8) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["19", "4"]]], ",", FractionBox["19", "4"], ",", "4", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["140821065", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox["z"]]]], " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "608"]], "-", RowBox[List["608", " ", SqrtBox["z"]]], "-", RowBox[List["4237", " ", "z"]], "-", RowBox[List["4237", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["39102", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["39102", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["940515", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["940515", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["3407304", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3407304", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["5018832", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["5018832", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["3357120", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["3357120", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["848640", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["848640", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "608"]], "-", RowBox[List["4085", " ", "z"]], "-", RowBox[List["38000", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["149553", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2772390", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["8664144", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["11525280", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["7138560", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["1697280", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 19 4 , 19 4 ; 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["19", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["19", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 140821065 π z + 1 z 3 ( 256 ( ( 848640 z 15 / 2 + 848640 z 7 - 3357120 z 13 / 2 - 3357120 z 6 + 5018832 z 11 / 2 + 5018832 z 5 - 3407304 z 9 / 2 - 3407304 z 4 + 940515 z 7 / 2 + 940515 z 3 - 39102 z 5 / 2 - 39102 z 2 - 4237 z 3 / 2 - 4237 z - 608 z - 608 ) E ( 2 z z + 1 ) - ( 1697280 z 8 - 7138560 z 7 + 11525280 z 6 - 8664144 z 5 + 2772390 z 4 - 149553 z 3 - 38000 z 2 - 4085 z - 608 ) K ( 2 z z + 1 ) ) ) HypergeometricPFQ -1 19 4 19 4 4 z 1 140821065 z 1 2 1 1 2 z 3 -1 256 848640 z 15 2 848640 z 7 -1 3357120 z 13 2 -1 3357120 z 6 5018832 z 11 2 5018832 z 5 -1 3407304 z 9 2 -1 3407304 z 4 940515 z 7 2 940515 z 3 -1 39102 z 5 2 -1 39102 z 2 -1 4237 z 3 2 -1 4237 z -1 608 z 1 2 -608 EllipticE 2 z 1 2 z 1 2 1 -1 -1 1697280 z 8 -1 7138560 z 7 11525280 z 6 -1 8664144 z 5 2772390 z 4 -1 149553 z 3 -1 38000 z 2 -1 4085 z -608 EllipticK 2 z 1 2 z 1 2 1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["19", "4"]]], ",", FractionBox["19", "4"], ",", "4", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "608"]], "-", RowBox[List["608", " ", SqrtBox["z"]]], "-", RowBox[List["4237", " ", "z"]], "-", RowBox[List["4237", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["39102", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["39102", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["940515", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["940515", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["3407304", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3407304", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["5018832", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["5018832", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["3357120", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["3357120", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["848640", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["848640", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "608"]], "-", RowBox[List["4085", " ", "z"]], "-", RowBox[List["38000", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["149553", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2772390", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["8664144", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["11525280", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["7138560", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["1697280", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]]]], ")"]]]], RowBox[List["140821065", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox["z"]]]], " ", SuperscriptBox["z", "3"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02