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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/2, 11/4, 6, z] == (1/(19845 Pi Sqrt[1 + Sqrt[1 - z]] z^5)) (512 Sqrt[2] (-2 (-2048 + 4928 z - 3252 z^2 + 150 z^3 + 75 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (-2048 + 4928 z - 3252 z^2 + 150 z^3 + 75 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-2048 + 4928 z - 3252 z^2 + 150 z^3 + 75 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-2048 + 4928 z - 3252 z^2 + 150 z^3 + 75 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-2048 + 4928 z - 3252 z^2 + 150 z^3 + 75 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (2048 - 3904 z + 1620 z^2 + 210 z^3 + 75 z^4) 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 ; 6 ; 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["6", 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 19845 π 1 - z + 1 z 5 ( 512 2 ( - 2 1 - z ( 75 z 4 + 150 z 3 - 3252 z 2 + 4928 z - 2048 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - 2 ( 75 z 4 + 150 z 3 - 3252 z 2 + 4928 z - 2048 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z ( 75 z 4 + 150 z 3 - 3252 z 2 + 4928 z - 2048 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z 4 ( 75 z 4 + 150 z 3 - 3252 z 2 + 4928 z - 2048 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 75 z 4 + 150 z 3 - 3252 z 2 + 4928 z - 2048 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - ( 1 - z ) 3 / 4 ( 75 z 4 + 210 z 3 + 1620 z 2 - 3904 z + 2048 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ 1 2 11 4 6 z 1 19845 1 -1 z 1 2 1 1 2 z 5 -1 512 2 1 2 -2 1 -1 z 1 2 75 z 4 150 z 3 -1 3252 z 2 4928 z -2048 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 2 75 z 4 150 z 3 -1 3252 z 2 4928 z -2048 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 2 75 z 4 150 z 3 -1 3252 z 2 4928 z -2048 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 75 z 4 150 z 3 -1 3252 z 2 4928 z -2048 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 75 z 4 150 z 3 -1 3252 z 2 4928 z -2048 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 3 4 75 z 4 210 z 3 1620 z 2 -1 3904 z 2048 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