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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.br19.01

 Input Form

 Hypergeometric2F1[-(11/8), -(1/8), 3, z] == (1/(863379 Pi z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-88 + 627 z + 8370 z^2 + 51 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (11 + 2178 z + 51 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-88 + 627 z + 8370 z^2 + 51 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (55 - 7128 z - 1989 z^2 + 102 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

 Standard Form

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 MathML Form

 2 F 1 ( - 11 8 , - 1 8 ; 3 ; 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["11", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["3", 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 863379 π z 2 ( 128 2 3 / 4 1 - z + 1 4 ( 4 ( 51 z 3 + 8370 z 2 + 627 z - 88 ) E ( 1 2 - 1 2 1 - z + 1 ) + 3 2 1 - z + 1 1 - z ( 51 z 2 + 2178 z + 11 ) K ( 1 2 - 1 2 1 - z + 1 ) - 2 ( 51 z 3 + 8370 z 2 + 627 z - 88 ) K ( 1 2 - 1 2 1 - z + 1 ) + 2 1 - z + 1 ( 102 z 3 - 1989 z 2 - 7128 z + 55 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ -1 11 8 -1 1 8 3 z 1 863379 z 2 -1 128 2 3 4 1 -1 z 1 2 1 1 4 4 51 z 3 8370 z 2 627 z -88 EllipticE 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 3 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 51 z 2 2178 z 11 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 2 51 z 3 8370 z 2 627 z -88 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 2 1 2 1 -1 z 1 2 1 1 2 102 z 3 -1 1989 z 2 -1 7128 z 55 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02