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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(3/2), 17/4, 2, z] == (1/(585 Pi Sqrt[1 + Sqrt[1 - z]] z)) (Sqrt[2] ((2 (-36 + 2134 z - 6391 z^2 + 4389 z^3) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (1 - z)^(3/4) + (2 (-36 + 2134 z - 6391 z^2 + 4389 z^3) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (1 - z)^(1/4) + (36 - 946 z + 1463 z^2) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - ((-36 + 2134 z - 6391 z^2 + 4389 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (1 - z)^(3/4) - ((-36 + 2134 z - 6391 z^2 + 4389 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ Sqrt[1 - z] - ((-36 + 2134 z - 6391 z^2 + 4389 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (1 - z)^(1/4)))

 Standard Form

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 MathML Form

 2 F 1 ( - 3 2 , 17 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["3", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["17", "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] 1 585 π 1 - z + 1 z ( 2 ( 2 ( 4389 z 3 - 6391 z 2 + 2134 z - 36 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) 1 - z 4 + 2 ( 4389 z 3 - 6391 z 2 + 2134 z - 36 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ( 1 - z ) 3 / 4 + ( 1463 z 2 - 946 z + 36 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 4389 z 3 - 6391 z 2 + 2134 z - 36 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) 1 - z 4 - ( 4389 z 3 - 6391 z 2 + 2134 z - 36 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) 1 - z - ( 4389 z 3 - 6391 z 2 + 2134 z - 36 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ( 1 - z ) 3 / 4 ) ) HypergeometricPFQ -1 3 2 17 4 2 z 1 585 1 -1 z 1 2 1 1 2 z -1 2 1 2 2 4389 z 3 -1 6391 z 2 2134 z -36 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 -1 2 4389 z 3 -1 6391 z 2 2134 z -36 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 -1 1463 z 2 -1 946 z 36 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 4389 z 3 -1 6391 z 2 2134 z -36 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 -1 -1 4389 z 3 -1 6391 z 2 2134 z -36 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 2 -1 -1 4389 z 3 -1 6391 z 2 2134 z -36 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 -1 [/itex]

 Rule Form

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

 2007-05-02