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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(13/4), -(1/4), 3, -z] == (1/(208845 Pi z^2 Sqrt[1 + Sqrt[1 + z]])) (64 Sqrt[2] ((-(52 + 611 z - 13175 z^2 + 1289 z^3 + 271 z^4 + 32 z^5)) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (52 + 611 z - 13175 z^2 + 1289 z^3 + 271 z^4 + 32 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (26 + 299 z - 3396 z^2 + 31 z^3 + 4 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (52 + 611 z - 13175 z^2 + 1289 z^3 + 271 z^4 + 32 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))

 Standard Form

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 MathML Form

 2 F 1 ( - 13 4 , - 1 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[RowBox[List["-", FractionBox["13", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "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 208845 π z 2 z + 1 + 1 ( 64 2 ( - z + 1 ( 32 z 5 + 271 z 4 + 1289 z 3 - 13175 z 2 + 611 z + 52 ) E ( z + 1 - 1 z + 1 + 1 ) - ( 32 z 5 + 271 z 4 + 1289 z 3 - 13175 z 2 + 611 z + 52 ) E ( z + 1 - 1 z + 1 + 1 ) + 2 z + 1 ( 4 z 4 + 31 z 3 - 3396 z 2 + 299 z + 26 ) K ( z + 1 - 1 z + 1 + 1 ) + ( 32 z 5 + 271 z 4 + 1289 z 3 - 13175 z 2 + 611 z + 52 ) K ( z + 1 - 1 z + 1 + 1 ) ) ) HypergeometricPFQ -1 13 4 -1 1 4 3 -1 z 1 208845 z 2 z 1 1 2 1 1 2 -1 64 2 1 2 -1 z 1 1 2 32 z 5 271 z 4 1289 z 3 -1 13175 z 2 611 z 52 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 -1 32 z 5 271 z 4 1289 z 3 -1 13175 z 2 611 z 52 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 2 z 1 1 2 4 z 4 31 z 3 -1 3396 z 2 299 z 26 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 32 z 5 271 z 4 1289 z 3 -1 13175 z 2 611 z 52 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