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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.afp0.01

 Input Form

 Hypergeometric2F1[-(3/2), 17/4, 4, z] == (1/(61425 Pi Sqrt[1 + Sqrt[1 - z]] z^3)) (8 Sqrt[2] (-2 (1 - z)^(1/4) (128 + 408 z + 1584 z^2 - 23870 z^3 + 21945 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (128 + 408 z + 1584 z^2 - 23870 z^3 + 21945 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (128 + 344 z + 1368 z^2 - 9350 z^3 + 7315 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (128 + 408 z + 1584 z^2 - 23870 z^3 + 21945 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (128 + 408 z + 1584 z^2 - 23870 z^3 + 21945 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (128 + 408 z + 1584 z^2 - 23870 z^3 + 21945 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 3 2 , 17 4 ; 4 ; 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["4", 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 61425 π 1 - z + 1 z 3 ( 8 2 ( - 2 ( 1 - z ) 3 / 4 ( 21945 z 4 - 23870 z 3 + 1584 z 2 + 408 z + 128 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 2 1 - z 4 ( 21945 z 4 - 23870 z 3 + 1584 z 2 + 408 z + 128 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 7315 z 4 - 9350 z 3 + 1368 z 2 + 344 z + 128 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 1 - z ) 3 / 4 ( 21945 z 4 - 23870 z 3 + 1584 z 2 + 408 z + 128 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z ( 21945 z 4 - 23870 z 3 + 1584 z 2 + 408 z + 128 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z 4 ( 21945 z 4 - 23870 z 3 + 1584 z 2 + 408 z + 128 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) HypergeometricPFQ -1 3 2 17 4 4 z 1 61425 1 -1 z 1 2 1 1 2 z 3 -1 8 2 1 2 -2 1 -1 z 3 4 21945 z 4 -1 23870 z 3 1584 z 2 408 z 128 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 2 1 -1 z 1 4 21945 z 4 -1 23870 z 3 1584 z 2 408 z 128 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 7315 z 4 -1 9350 z 3 1368 z 2 344 z 128 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 21945 z 4 -1 23870 z 3 1584 z 2 408 z 128 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 2 21945 z 4 -1 23870 z 3 1584 z 2 408 z 128 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 21945 z 4 -1 23870 z 3 1584 z 2 408 z 128 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 [/itex]

 Rule Form

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

 2007-05-02