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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c5co.01

 Input Form

 Hypergeometric2F1[15/8, 29/8, 3, z] == (1/(9555 Pi (-1 + z)^3 z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (8 (-1 + z) (20 - 35 z + 21 z^2) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (5 + 7 z) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (5 - 35 z + 14 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 4 (-1 + z) (20 - 35 z + 21 z^2) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

 Standard Form

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 MathML Form

 2 F 1 ( 15 8 , 29 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[FractionBox["15", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["29", "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 9555 π ( z - 1 ) 3 z 2 ( 128 2 3 / 4 1 - z + 1 4 ( 8 ( z - 1 ) ( 21 z 2 - 35 z + 20 ) E ( 1 2 - 1 2 1 - z + 1 ) - 5 2 1 - z + 1 ( z - 1 ) ( 7 z + 5 ) K ( 1 2 - 1 2 1 - z + 1 ) + 3 2 1 - z + 1 1 - z ( 14 z 2 - 35 z + 5 ) K ( 1 2 - 1 2 1 - z + 1 ) - 4 ( z - 1 ) ( 21 z 2 - 35 z + 20 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ 15 8 29 8 3 z 1 9555 z -1 3 z 2 -1 128 2 3 4 1 -1 z 1 2 1 1 4 8 z -1 21 z 2 -1 35 z 20 EllipticE 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 z -1 7 z 5 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 3 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 14 z 2 -1 35 z 5 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 4 z -1 21 z 2 -1 35 z 20 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