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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[7/4, 11/2, 5, z] == (128 Sqrt[2] (-2 (1 - z)^(3/2) (256 - 192 z - 108 z^2 - 112 z^3 + 231 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 (-1 + z) (256 - 192 z - 108 z^2 - 112 z^3 + 231 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (256 - 320 z - 36 z^2 - 52 z^3 + 77 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(5/4) (256 - 192 z - 108 z^2 - 112 z^3 + 231 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/2) (256 - 192 z - 108 z^2 - 112 z^3 + 231 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-1 + z) (256 - 192 z - 108 z^2 - 112 z^3 + 231 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (14175 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^3 z^4)

 Standard Form

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 MathML Form

 2 F 1 ( 7 4 , 11 2 ; 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["5", 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] ( 128 2 ( - 2 ( 231 z 4 - 112 z 3 - 108 z 2 - 192 z + 256 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 + ( 231 z 4 - 112 z 3 - 108 z 2 - 192 z + 256 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 + ( 231 z 4 - 112 z 3 - 108 z 2 - 192 z + 256 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 5 / 4 + ( 77 z 4 - 52 z 3 - 36 z 2 - 320 z + 256 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 4 + 2 ( z - 1 ) ( 231 z 4 - 112 z 3 - 108 z 2 - 192 z + 256 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - ( z - 1 ) ( 231 z 4 - 112 z 3 - 108 z 2 - 192 z + 256 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) / ( 14175 π 1 - z + 1 ( z - 1 ) 3 z 4 ) HypergeometricPFQ 7 4 11 2 5 z 128 2 1 2 -2 231 z 4 -1 112 z 3 -1 108 z 2 -1 192 z 256 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 231 z 4 -1 112 z 3 -1 108 z 2 -1 192 z 256 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 231 z 4 -1 112 z 3 -1 108 z 2 -1 192 z 256 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 5 4 77 z 4 -1 52 z 3 -1 36 z 2 -1 320 z 256 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 2 z -1 231 z 4 -1 112 z 3 -1 108 z 2 -1 192 z 256 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 z -1 231 z 4 -1 112 z 3 -1 108 z 2 -1 192 z 256 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 14175 1 -1 z 1 2 1 1 2 z -1 3 z 4 -1 [/itex]

 Rule Form

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

 2007-05-02