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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.brb4.01

 Input Form

 Hypergeometric2F1[-(11/8), 17/8, 2, z] == -((1/(1881 Pi (1 + Sqrt[1 - z])^(1/4) z)) (16 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (11 - 328 z + 320 z^2) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (11 (1 + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + Sqrt[1 - z]) - (97 + 328 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 328 Sqrt[1 - z]) z + 80 (1 + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 4 Sqrt[1 - z]) z^2) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])))

 Standard Form

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 MathML Form

 2 F 1 ( - 11 8 , 17 8 ; 2 ; 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[FractionBox["17", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["2", 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 1881 π 1 - z + 1 4 z ( 16 2 4 ( 2 2 1 - z + 1 1 - z 4 ( 320 z 2 - 328 z + 11 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) - ( 80 ( 4 2 1 - z 4 1 - z + 1 + 4 1 - z + 1 ) z 2 - ( 328 2 1 - z 4 1 - z + 1 + 328 1 - z + 97 ) z + 11 ( 2 1 - z 4 1 - z + 1 + 1 - z + 1 ) ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ) ) HypergeometricPFQ -1 11 8 17 8 2 z -1 1 1881 1 -1 z 1 2 1 1 4 z -1 16 2 1 4 2 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 320 z 2 -1 328 z 11 EllipticE 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 80 4 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 4 1 -1 z 1 2 1 z 2 -1 328 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 328 1 -1 z 1 2 97 z 11 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 1 -1 z 1 2 1 EllipticK 1 2 -1 1 -1 z 1 4 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