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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[23/4, 23/4, 1, -z] == (1/(7315 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] ((2 (5021 - 65820 z + 141198 z^2 - 65820 z^3 + 5021 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^10 + (2 (5021 - 65820 z + 141198 z^2 - 65820 z^3 + 5021 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(19/2) - (2 (5021 - 65820 z + 141198 z^2 - 65820 z^3 + 5021 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^10 - (1/(1 + z)^(21/2)) ((2727 + 40479 z - 386810 z^2 + 537566 z^3 - 162077 z^4 + 7315 z^5) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])))

 Standard Form

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 MathML Form

 2 F 1 ( 23 4 , 23 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["23", "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["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 7315 π z + 1 + 1 ( 2 2 ( 2 ( 5021 z 4 - 65820 z 3 + 141198 z 2 - 65820 z + 5021 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 19 / 2 + 2 ( 5021 z 4 - 65820 z 3 + 141198 z 2 - 65820 z + 5021 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 10 - 2 ( 5021 z 4 - 65820 z 3 + 141198 z 2 - 65820 z + 5021 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 10 - ( 7315 z 5 - 162077 z 4 + 537566 z 3 - 386810 z 2 + 40479 z + 2727 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 21 / 2 ) ) HypergeometricPFQ 23 4 23 4 1 -1 z 1 7315 z 1 1 2 1 1 2 -1 2 2 1 2 2 5021 z 4 -1 65820 z 3 141198 z 2 -1 65820 z 5021 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 19 2 -1 2 5021 z 4 -1 65820 z 3 141198 z 2 -1 65820 z 5021 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 10 -1 -1 2 5021 z 4 -1 65820 z 3 141198 z 2 -1 65820 z 5021 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 10 -1 -1 7315 z 5 -1 162077 z 4 537566 z 3 -1 386810 z 2 40479 z 2727 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 21 2 -1 [/itex]

 Rule Form

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

 2007-05-02