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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[23/4, 23/4, 2, -z] == (1/(138985 Pi z Sqrt[1 + Sqrt[1 + z]])) (8 Sqrt[2] (-(((385 - 35572 z + 141198 z^2 - 96068 z^3 + 9657 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^9) - ((385 - 35572 z + 141198 z^2 - 96068 z^3 + 9657 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(17/2) + ((385 - 35572 z + 141198 z^2 - 96068 z^3 + 9657 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^9 + ((385 - 537 z - 127646 z^2 + 304294 z^3 - 127427 z^4 + 7315 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(19/2)))

 Standard Form

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 MathML Form

 2 F 1 ( 23 4 , 23 4 ; 2 ; - 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["2", 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 138985 π z z + 1 + 1 ( 8 2 ( - ( 9657 z 4 - 96068 z 3 + 141198 z 2 - 35572 z + 385 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 17 / 2 - ( 9657 z 4 - 96068 z 3 + 141198 z 2 - 35572 z + 385 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 9 + ( 9657 z 4 - 96068 z 3 + 141198 z 2 - 35572 z + 385 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 9 + ( 7315 z 5 - 127427 z 4 + 304294 z 3 - 127646 z 2 - 537 z + 385 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 19 / 2 ) ) HypergeometricPFQ 23 4 23 4 2 -1 z 1 138985 z z 1 1 2 1 1 2 -1 8 2 1 2 -1 9657 z 4 -1 96068 z 3 141198 z 2 -1 35572 z 385 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 17 2 -1 -1 9657 z 4 -1 96068 z 3 141198 z 2 -1 35572 z 385 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 9 -1 9657 z 4 -1 96068 z 3 141198 z 2 -1 35572 z 385 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 9 -1 7315 z 5 -1 127427 z 4 304294 z 3 -1 127646 z 2 -1 537 z 385 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 19 2 -1 [/itex]

 Rule Form

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

 2007-05-02