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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/8, 5/8, 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (128 - 395 z + 447 z^2) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (128 (1 + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + Sqrt[1 - z]) - (443 + 395 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 395 Sqrt[1 - z]) z + (582 + 447 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 447 Sqrt[1 - z]) z^2 - 627 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (504735 Pi (1 + Sqrt[1 - z])^(1/4) z^3)

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 5 8 ; 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], 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 504735 π 1 - z + 1 4 z 3 ( 2048 2 4 ( 2 2 1 - z + 1 1 - z 4 ( 447 z 2 - 395 z + 128 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) - ( - 627 z 3 + ( 447 2 1 - z 4 1 - z + 1 + 447 1 - z + 582 ) z 2 - ( 395 2 1 - z 4 1 - z + 1 + 395 1 - z + 443 ) z + 128 ( 2 1 - z 4 1 - z + 1 + 1 - z + 1 ) ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ) ) HypergeometricPFQ 1 8 5 8 4 z 1 504735 1 -1 z 1 2 1 1 4 z 3 -1 2048 2 1 4 2 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 447 z 2 -1 395 z 128 EllipticE 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 -627 z 3 447 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 447 1 -1 z 1 2 582 z 2 -1 395 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 395 1 -1 z 1 2 443 z 128 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