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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(5/2), 3/4, 2, z] == (1/(105 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z)) (2 (120 + 232 z - 166 z^2 + 45 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (120 + 232 z - 166 z^2 + 45 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (120 + 232 z - 166 z^2 + 45 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (120 + 232 z - 166 z^2 + 45 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (120 + 232 z - 166 z^2 + 45 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-120 + 128 z - 130 z^2 + 45 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])

 Standard Form

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 MathML Form

 2 F 1 ( - 5 2 , 3 4 ; 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["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "4"], 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] 1 105 2 π 1 - z + 1 z ( 2 1 - z ( 45 z 3 - 166 z 2 + 232 z + 120 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 2 ( 45 z 3 - 166 z 2 + 232 z + 120 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - 1 - z ( 45 z 3 - 166 z 2 + 232 z + 120 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - 1 - z 4 ( 45 z 3 - 166 z 2 + 232 z + 120 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - ( 45 z 3 - 166 z 2 + 232 z + 120 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 1 - z ) 3 / 4 ( 45 z 3 - 130 z 2 + 128 z - 120 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) HypergeometricPFQ -1 5 2 3 4 2 z 1 105 2 1 2 1 -1 z 1 2 1 1 2 z -1 2 1 -1 z 1 2 45 z 3 -1 166 z 2 232 z 120 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 2 45 z 3 -1 166 z 2 232 z 120 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 1 2 45 z 3 -1 166 z 2 232 z 120 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 1 4 45 z 3 -1 166 z 2 232 z 120 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 45 z 3 -1 166 z 2 232 z 120 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 45 z 3 -1 130 z 2 128 z -120 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