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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/2, 11/4, 5, z] == (1/(3675 Pi Sqrt[1 + Sqrt[1 - z]] z^4)) (256 Sqrt[2] (-2 (384 - 512 z + 40 z^2 + 25 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (384 - 512 z + 40 z^2 + 25 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (384 - 512 z + 40 z^2 + 25 z^3) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (384 - 512 z + 40 z^2 + 25 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (384 - 512 z + 40 z^2 + 25 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-384 + 320 z + 60 z^2 + 25 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 2 , 11 4 ; 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["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "4"], 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] 1 3675 π 1 - z + 1 z 4 ( 256 2 ( - 2 1 - z ( 25 z 3 + 40 z 2 - 512 z + 384 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - 2 ( 25 z 3 + 40 z 2 - 512 z + 384 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z ( 25 z 3 + 40 z 2 - 512 z + 384 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z 4 ( 25 z 3 + 40 z 2 - 512 z + 384 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 25 z 3 + 40 z 2 - 512 z + 384 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - ( 1 - z ) 3 / 4 ( 25 z 3 + 60 z 2 + 320 z - 384 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ 1 2 11 4 5 z 1 3675 1 -1 z 1 2 1 1 2 z 4 -1 256 2 1 2 -2 1 -1 z 1 2 25 z 3 40 z 2 -1 512 z 384 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 2 25 z 3 40 z 2 -1 512 z 384 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 2 25 z 3 40 z 2 -1 512 z 384 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 25 z 3 40 z 2 -1 512 z 384 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 25 z 3 40 z 2 -1 512 z 384 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 3 4 25 z 3 60 z 2 320 z -384 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02