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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ak0a.01

 Input Form

 Hypergeometric2F1[5/4, 9/2, 2, z] == (2 (1 - z)^(1/4) (120 + 232 z - 166 z^2 + 45 z^3) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (120 + 232 z - 166 z^2 + 45 z^3) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-1 + z) (120 - 128 z + 130 z^2 - 45 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (120 + 232 z - 166 z^2 + 45 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (120 + 232 z - 166 z^2 + 45 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (120 + 232 z - 166 z^2 + 45 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (105 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^4 z)

 Standard Form

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 MathML Form

 2 F 1 ( 5 4 , 9 2 ; 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "2"], 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] ( 2 ( 1 - z ) 3 / 4 ( 45 z 3 - 166 z 2 + 232 z + 120 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 2 1 - z 4 ( 45 z 3 - 166 z 2 + 232 z + 120 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( z - 1 ) ( - 45 z 3 + 130 z 2 - 128 z + 120 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 1 - z ) 3 / 4 ( 45 z 3 - 166 z 2 + 232 z + 120 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z ( 45 z 3 - 166 z 2 + 232 z + 120 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z 4 ( 45 z 3 - 166 z 2 + 232 z + 120 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) / ( 105 2 π 1 - z + 1 ( z - 1 ) 4 z ) HypergeometricPFQ 5 4 9 2 2 z 2 1 -1 z 3 4 45 z 3 -1 166 z 2 232 z 120 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 2 1 -1 z 1 4 45 z 3 -1 166 z 2 232 z 120 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 z -1 -45 z 3 130 z 2 -1 128 z 120 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 3 4 45 z 3 -1 166 z 2 232 z 120 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 2 45 z 3 -1 166 z 2 232 z 120 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 4 45 z 3 -1 166 z 2 232 z 120 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 105 2 1 2 1 -1 z 1 2 1 1 2 z -1 4 z -1 [/itex]

 Rule Form

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

 2007-05-02