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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.aj6y.01

 Input Form

 Hypergeometric2F1[3/4, 19/4, 1, -z] == (1/(1155 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] ((4 (183 + 213 z + 132 z^2 + 32 z^3) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^4 + (4 (183 + 213 z + 132 z^2 + 32 z^3) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])/(1 + z)^(7/2) - (4 (183 + 213 z + 132 z^2 + 32 z^3) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])/(1 + z)^4 - ((-423 + 246 z + 141 z^2 + 32 z^3) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])/(1 + z)^(9/2)))

 Standard Form

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 MathML Form

 2 F 1 ( 3 4 , 19 4 ; 1 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["19", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["1", 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 1155 π z + 1 + 1 ( 2 2 ( 4 ( 32 z 3 + 132 z 2 + 213 z + 183 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 7 / 2 + 4 ( 32 z 3 + 132 z 2 + 213 z + 183 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 4 - 4 ( 32 z 3 + 132 z 2 + 213 z + 183 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 4 - ( 32 z 3 + 141 z 2 + 246 z - 423 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 9 / 2 ) ) HypergeometricPFQ 3 4 19 4 1 -1 z 1 1155 z 1 1 2 1 1 2 -1 2 2 1 2 4 32 z 3 132 z 2 213 z 183 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 7 2 -1 4 32 z 3 132 z 2 213 z 183 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 4 -1 -1 4 32 z 3 132 z 2 213 z 183 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 4 -1 -1 32 z 3 141 z 2 246 z -423 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 9 2 -1 [/itex]

 Rule Form

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

 2007-05-02