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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[11/4, 23/4, 3, -z] == (1/(65835 Pi z^2 Sqrt[1 + Sqrt[1 + z]])) (64 Sqrt[2] (((-44 - 341 z + 582 z^2 + 191 z^3 + 32 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^5 + ((-44 - 341 z + 582 z^2 + 191 z^3 + 32 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(9/2) - (2 (-22 - 187 z - 864 z^2 + 25 z^3 + 4 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(11/2) - ((-44 - 341 z + 582 z^2 + 191 z^3 + 32 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^5))

 Standard Form

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 MathML Form

 2 F 1 ( 11 4 , 23 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["11", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["23", "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[RowBox[List["-", "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 65835 π z 2 z + 1 + 1 ( 64 2 ( ( 32 z 4 + 191 z 3 + 582 z 2 - 341 z - 44 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 9 / 2 + ( 32 z 4 + 191 z 3 + 582 z 2 - 341 z - 44 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 5 - 2 ( 4 z 4 + 25 z 3 - 864 z 2 - 187 z - 22 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 11 / 2 - ( 32 z 4 + 191 z 3 + 582 z 2 - 341 z - 44 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 5 ) ) HypergeometricPFQ 11 4 23 4 3 -1 z 1 65835 z 2 z 1 1 2 1 1 2 -1 64 2 1 2 32 z 4 191 z 3 582 z 2 -1 341 z -44 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 9 2 -1 32 z 4 191 z 3 582 z 2 -1 341 z -44 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 5 -1 -1 2 4 z 4 25 z 3 -1 864 z 2 -1 187 z -22 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 11 2 -1 -1 32 z 4 191 z 3 582 z 2 -1 341 z -44 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 5 -1 [/itex]

 Rule Form

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

 2007-05-02