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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ab0w.01

 Input Form

 Hypergeometric2F1[-(15/4), -(15/4), 2, -z] == (1/(138985 Pi z Sqrt[1 + Sqrt[1 + z]])) (8 Sqrt[2] ((-Sqrt[1 + z]) (385 - 35572 z + 141198 z^2 - 96068 z^3 + 9657 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (385 - 35187 z + 105626 z^2 + 45130 z^3 - 86411 z^4 + 9657 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (385 - 35572 z + 141198 z^2 - 96068 z^3 + 9657 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (385 - 537 z - 127646 z^2 + 304294 z^3 - 127427 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 ( - 15 4 , - 15 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[RowBox[List["-", FractionBox["15", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["15", "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 ( - z + 1 ( 9657 z 4 - 96068 z 3 + 141198 z 2 - 35572 z + 385 ) E ( z + 1 - 1 z + 1 + 1 ) - ( 9657 z 5 - 86411 z 4 + 45130 z 3 + 105626 z 2 - 35187 z + 385 ) E ( z + 1 - 1 z + 1 + 1 ) + z + 1 ( 9657 z 4 - 96068 z 3 + 141198 z 2 - 35572 z + 385 ) K ( z + 1 - 1 z + 1 + 1 ) + ( 7315 z 5 - 127427 z 4 + 304294 z 3 - 127646 z 2 - 537 z + 385 ) K ( z + 1 - 1 z + 1 + 1 ) ) ) HypergeometricPFQ -1 15 4 -1 15 4 2 -1 z 1 138985 z z 1 1 2 1 1 2 -1 8 2 1 2 -1 z 1 1 2 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 -1 9657 z 5 -1 86411 z 4 45130 z 3 105626 z 2 -1 35187 z 385 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 1 2 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 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 [/itex]

 Rule Form

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

 2007-05-02