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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.br6n.01

 Input Form

 Hypergeometric2F1[-(11/8), 9/8, 2, z] == -((1/(627 Pi (1 + Sqrt[1 - z])^(1/4) z)) (16 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (33 - 91 z + 48 z^2) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (33 (1 + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + Sqrt[1 - z]) - (25 + 91 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 91 Sqrt[1 - z]) z + 12 (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 , 9 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["9", "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] - 1 627 π 1 - z + 1 4 z ( 16 2 4 ( 2 2 1 - z + 1 1 - z 4 ( 48 z 2 - 91 z + 33 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) - ( 12 ( 4 2 1 - z 4 1 - z + 1 + 4 1 - z + 1 ) z 2 - ( 91 2 1 - z 4 1 - z + 1 + 91 1 - z + 25 ) z + 33 ( 2 1 - z 4 1 - z + 1 + 1 - z + 1 ) ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ) ) HypergeometricPFQ -1 11 8 9 8 2 z -1 1 627 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 48 z 2 -1 91 z 33 EllipticE 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 12 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 91 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 91 1 -1 z 1 2 25 z 33 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