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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[13/4, 21/4, 3, -z] == (1/(9945 Pi z^2 Sqrt[1 + Sqrt[1 + z]])) (64 Sqrt[2] (-((2 (2 + 19 z - 302 z^2 + 19 z^3 + 2 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(11/2)) - (2 (2 + 19 z - 302 z^2 + 19 z^3 + 2 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^5 + ((4 + 37 z - 302 z^2 + z^3) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])/(1 + z)^5 + (2 (2 + 19 z - 302 z^2 + 19 z^3 + 2 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(11/2)))

 Standard Form

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 MathML Form

 2 F 1 ( 13 4 , 21 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[FractionBox["13", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "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 9945 π z 2 z + 1 + 1 ( 64 2 ( - 2 ( 2 z 4 + 19 z 3 - 302 z 2 + 19 z + 2 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 5 - 2 ( 2 z 4 + 19 z 3 - 302 z 2 + 19 z + 2 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 11 / 2 + ( z 3 - 302 z 2 + 37 z + 4 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 5 + 2 ( 2 z 4 + 19 z 3 - 302 z 2 + 19 z + 2 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 11 / 2 ) ) HypergeometricPFQ 13 4 21 4 3 -1 z 1 9945 z 2 z 1 1 2 1 1 2 -1 64 2 1 2 -1 2 2 z 4 19 z 3 -1 302 z 2 19 z 2 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 5 -1 -1 2 2 z 4 19 z 3 -1 302 z 2 19 z 2 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 11 2 -1 z 3 -1 302 z 2 37 z 4 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 5 -1 2 2 z 4 19 z 3 -1 302 z 2 19 z 2 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 11 2 -1 [/itex]

 Rule Form

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

 2007-05-02