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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ak3a.01

 Input Form

 Hypergeometric2F1[5/4, 21/4, 1, -z] == (1/(9945 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] (-((2 (-12167 + 4986 z + 2985 z^2 + 1144 z^3 + 192 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(11/2)) - (2 (-12167 + 4986 z + 2985 z^2 + 1144 z^3 + 192 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^5 + ((-14389 + 1138 z + 503 z^2 + 96 z^3) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])/(1 + z)^5 + (2 (-12167 + 4986 z + 2985 z^2 + 1144 z^3 + 192 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(11/2)))

 Standard Form

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 MathML Form

 2 F 1 ( 5 4 , 21 4 ; 1 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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 9945 π z + 1 + 1 ( 2 2 ( - 2 ( 192 z 4 + 1144 z 3 + 2985 z 2 + 4986 z - 12167 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 5 - 2 ( 192 z 4 + 1144 z 3 + 2985 z 2 + 4986 z - 12167 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 11 / 2 + ( 96 z 3 + 503 z 2 + 1138 z - 14389 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 5 + 2 ( 192 z 4 + 1144 z 3 + 2985 z 2 + 4986 z - 12167 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 11 / 2 ) ) HypergeometricPFQ 5 4 21 4 1 -1 z 1 9945 z 1 1 2 1 1 2 -1 2 2 1 2 -1 2 192 z 4 1144 z 3 2985 z 2 4986 z -12167 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 5 -1 -1 2 192 z 4 1144 z 3 2985 z 2 4986 z -12167 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 11 2 -1 96 z 3 503 z 2 1138 z -14389 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 5 -1 2 192 z 4 1144 z 3 2985 z 2 4986 z -12167 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 11 2 -1 [/itex]

 Rule Form

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

 2007-05-02