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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.akc4.01

 Input Form

 Hypergeometric2F1[3/2, 21/4, 3, z] == (32 Sqrt[2] (2 (1 - z)^(1/4) (90 - 180 z + 874 z^2 - 784 z^3 + 231 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (90 - 180 z + 874 z^2 - 784 z^3 + 231 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-1 + z) (-90 + 135 z - 199 z^2 + 77 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (90 - 180 z + 874 z^2 - 784 z^3 + 231 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (90 - 180 z + 874 z^2 - 784 z^3 + 231 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (90 - 180 z + 874 z^2 - 784 z^3 + 231 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (9945 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^4 z^2)

 Standard Form

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 MathML Form

 2 F 1 ( 3 2 , 21 4 ; 3 ; 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", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["3", 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] ( 32 2 ( 2 ( 1 - z ) 3 / 4 ( 231 z 4 - 784 z 3 + 874 z 2 - 180 z + 90 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 2 1 - z 4 ( 231 z 4 - 784 z 3 + 874 z 2 - 180 z + 90 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( z - 1 ) ( 77 z 3 - 199 z 2 + 135 z - 90 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 1 - z ) 3 / 4 ( 231 z 4 - 784 z 3 + 874 z 2 - 180 z + 90 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z ( 231 z 4 - 784 z 3 + 874 z 2 - 180 z + 90 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z 4 ( 231 z 4 - 784 z 3 + 874 z 2 - 180 z + 90 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) / ( 9945 π 1 - z + 1 ( z - 1 ) 4 z 2 ) HypergeometricPFQ 3 2 21 4 3 z 32 2 1 2 2 1 -1 z 3 4 231 z 4 -1 784 z 3 874 z 2 -1 180 z 90 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 2 1 -1 z 1 4 231 z 4 -1 784 z 3 874 z 2 -1 180 z 90 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 z -1 77 z 3 -1 199 z 2 135 z -90 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 3 4 231 z 4 -1 784 z 3 874 z 2 -1 180 z 90 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 2 231 z 4 -1 784 z 3 874 z 2 -1 180 z 90 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 4 231 z 4 -1 784 z 3 874 z 2 -1 180 z 90 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 9945 1 -1 z 1 2 1 1 2 z -1 4 z 2 -1 [/itex]

 Rule Form

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

 2007-05-02