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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[3/4, 3/2, 5, z] == -((1/(2925 Pi Sqrt[1 + Sqrt[1 - z]] z^4)) (512 Sqrt[2] (2 (1 + Sqrt[1 - z]) (-192 + 496 z - 385 z^2 + 60 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (192 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) - 16 (31 + 31 (1 - z)^(1/4) + 31 Sqrt[1 - z] + 25 (1 - z)^(3/4)) z + 5 (77 + 77 (1 - z)^(1/4) + 77 Sqrt[1 - z] + 43 (1 - z)^(3/4)) z^2 - 60 (1 + (1 - z)^(1/4) + Sqrt[1 - z]) z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])))

 Standard Form

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 MathML Form

 2 F 1 ( 3 4 , 3 2 ; 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["5", 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 2925 π 1 - z + 1 z 4 ( 512 2 ( 2 ( 1 - z + 1 ) ( 60 z 3 - 385 z 2 + 496 z - 192 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( - 60 ( 1 - z + 1 - z 4 + 1 ) z 3 + 5 ( 43 ( 1 - z ) 3 / 4 + 77 1 - z + 77 1 - z 4 + 77 ) z 2 - 16 ( 25 ( 1 - z ) 3 / 4 + 31 1 - z + 31 1 - z 4 + 31 ) z + 192 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ 3 4 3 2 5 z -1 1 2925 1 -1 z 1 2 1 1 2 z 4 -1 512 2 1 2 2 1 -1 z 1 2 1 60 z 3 -1 385 z 2 496 z -192 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -60 1 -1 z 1 2 1 -1 z 1 4 1 z 3 5 43 1 -1 z 3 4 77 1 -1 z 1 2 77 1 -1 z 1 4 77 z 2 -1 16 25 1 -1 z 3 4 31 1 -1 z 1 2 31 1 -1 z 1 4 31 z 192 1 -1 z 3 4 1 -1 z 1 2 1 -1 z 1 4 1 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02