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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ac29.01

 Input Form

 Hypergeometric2F1[-(7/2), 11/4, 3, z] == (1/(10395 Pi Sqrt[1 + Sqrt[1 - z]] z^2)) (Sqrt[2] (-2 (320 + 1360 z - 19344 z^2 + 41964 z^3 - 34476 z^4 + 9945 z^5) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (320 + 1360 z - 19344 z^2 + 41964 z^3 - 34476 z^4 + 9945 z^5) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (320 + 1520 z + 2256 z^2 - 20748 z^3 + 26520 z^4 - 9945 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (320 + 1360 z - 19344 z^2 + 41964 z^3 - 34476 z^4 + 9945 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (320 + 1360 z - 19344 z^2 + 41964 z^3 - 34476 z^4 + 9945 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (320 + 1360 z - 19344 z^2 + 41964 z^3 - 34476 z^4 + 9945 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))

 Standard Form

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 MathML Form

 2 F 1 ( - 7 2 , 11 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[RowBox[List["-", FractionBox["7", "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["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] 1 10395 π 1 - z + 1 z 2 ( 2 ( - 2 1 - z ( 9945 z 5 - 34476 z 4 + 41964 z 3 - 19344 z 2 + 1360 z + 320 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - 2 ( 9945 z 5 - 34476 z 4 + 41964 z 3 - 19344 z 2 + 1360 z + 320 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 1 - z ) 3 / 4 ( - 9945 z 5 + 26520 z 4 - 20748 z 3 + 2256 z 2 + 1520 z + 320 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z ( 9945 z 5 - 34476 z 4 + 41964 z 3 - 19344 z 2 + 1360 z + 320 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z 4 ( 9945 z 5 - 34476 z 4 + 41964 z 3 - 19344 z 2 + 1360 z + 320 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 9945 z 5 - 34476 z 4 + 41964 z 3 - 19344 z 2 + 1360 z + 320 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ -1 7 2 11 4 3 z 1 10395 1 -1 z 1 2 1 1 2 z 2 -1 2 1 2 -2 1 -1 z 1 2 9945 z 5 -1 34476 z 4 41964 z 3 -1 19344 z 2 1360 z 320 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 2 9945 z 5 -1 34476 z 4 41964 z 3 -1 19344 z 2 1360 z 320 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 -9945 z 5 26520 z 4 -1 20748 z 3 2256 z 2 1520 z 320 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 2 9945 z 5 -1 34476 z 4 41964 z 3 -1 19344 z 2 1360 z 320 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 9945 z 5 -1 34476 z 4 41964 z 3 -1 19344 z 2 1360 z 320 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 9945 z 5 -1 34476 z 4 41964 z 3 -1 19344 z 2 1360 z 320 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