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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(11/8), 31/8, 3, z] == (1/(13627845 Pi z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (616 + 3927 z - 51948 z^2 + 53040 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-77 - 36036 z + 53040 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-77 + 20790 z - 43056 z^2 + 21216 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (616 + 3927 z - 51948 z^2 + 53040 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 , 31 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[FractionBox["31", "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 13627845 π z 2 ( 128 2 3 / 4 1 - z + 1 4 ( - 4 ( 53040 z 3 - 51948 z 2 + 3927 z + 616 ) E ( 1 2 - 1 2 1 - z + 1 ) - 3 2 1 - z + 1 1 - z ( 53040 z 2 - 36036 z - 77 ) K ( 1 2 - 1 2 1 - z + 1 ) - 5 2 1 - z + 1 ( 21216 z 3 - 43056 z 2 + 20790 z - 77 ) K ( 1 2 - 1 2 1 - z + 1 ) + 2 ( 53040 z 3 - 51948 z 2 + 3927 z + 616 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ -1 11 8 31 8 3 z 1 13627845 z 2 -1 128 2 3 4 1 -1 z 1 2 1 1 4 -4 53040 z 3 -1 51948 z 2 3927 z 616 EllipticE 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 3 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 53040 z 2 -1 36036 z -77 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 5 2 1 2 1 -1 z 1 2 1 1 2 21216 z 3 -1 43056 z 2 20790 z -77 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 2 53040 z 3 -1 51948 z 2 3927 z 616 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