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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c3ky.01

 Input Form

 Hypergeometric2F1[11/8, 31/8, 4, z] == -((2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-128 + 27 z + 36 z^2) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (-128 (1 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) + 3 (25 + 9 Sqrt[1 - z] + 9 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + (39 + 36 Sqrt[1 - z] + 36 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 + 144 z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/(156975 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(5/4) z^3))

 Standard Form

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 MathML Form

 2 F 1 ( 11 8 , 31 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["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["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] - ( 2048 2 4 ( 2 2 - z + 1 - z + 1 ( 36 z 2 + 27 z - 128 ) E ( 1 2 - 1 - z 2 - z + 1 - z + 1 ) - ( 144 z 3 + ( 36 1 - z + 36 2 - z + 1 - z + 1 + 39 ) z 2 + 3 ( 9 1 - z + 9 2 - z + 1 - z + 1 + 25 ) z - 128 ( 1 - z + 2 - z + 1 - z + 1 + 1 ) ) K ( 1 2 - 1 - z 2 - z + 1 - z + 1 ) ) ) / ( 156975 π 1 - z + 1 4 ( 1 - z ) 5 / 4 z 3 ) HypergeometricPFQ 11 8 31 8 4 z -1 2048 2 1 4 2 2 1 2 -1 z 1 -1 z 1 2 1 1 2 36 z 2 27 z -128 EllipticE 1 2 -1 1 -1 z 1 2 2 1 2 -1 z 1 -1 z 1 2 1 1 2 -1 -1 144 z 3 36 1 -1 z 1 2 36 2 1 2 -1 z 1 -1 z 1 2 1 1 2 39 z 2 3 9 1 -1 z 1 2 9 2 1 2 -1 z 1 -1 z 1 2 1 1 2 25 z -1 128 1 -1 z 1 2 2 1 2 -1 z 1 -1 z 1 2 1 1 2 1 EllipticK 1 2 -1 1 -1 z 1 2 2 1 2 -1 z 1 -1 z 1 2 1 1 2 -1 156975 1 -1 z 1 2 1 1 4 1 -1 z 5 4 z 3 -1 [/itex]

 Rule Form

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

 2007-05-02