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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ajb3.01

 Input Form

 Hypergeometric2F1[3/4, 23/4, 5, -z] == (4096 Sqrt[2] (((-384 + 368 z - 429 z^2 + 672 z^3 + 2048 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z) + ((-384 + 368 z - 429 z^2 + 672 z^3 + 2048 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/Sqrt[1 + z] - (2 (-192 + 40 z - 63 z^2 + 156 z^3 + 256 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(3/2) - ((-384 + 368 z - 429 z^2 + 672 z^3 + 2048 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)))/ (4279275 Pi z^4 Sqrt[1 + Sqrt[1 + z]])

 Standard Form

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 MathML Form

 2 F 1 ( 3 4 , 23 4 ; 5 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "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["5", 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 4279275 π z 4 z + 1 + 1 ( 4096 2 ( ( 2048 z 4 + 672 z 3 - 429 z 2 + 368 z - 384 ) E ( z + 1 - 1 z + 1 + 1 ) z + 1 + ( 2048 z 4 + 672 z 3 - 429 z 2 + 368 z - 384 ) E ( z + 1 - 1 z + 1 + 1 ) z + 1 - 2 ( 256 z 4 + 156 z 3 - 63 z 2 + 40 z - 192 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 3 / 2 - ( 2048 z 4 + 672 z 3 - 429 z 2 + 368 z - 384 ) K ( z + 1 - 1 z + 1 + 1 ) z + 1 ) ) HypergeometricPFQ 3 4 23 4 5 -1 z 1 4279275 z 4 z 1 1 2 1 1 2 -1 4096 2 1 2 2048 z 4 672 z 3 -1 429 z 2 368 z -384 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 1 2 -1 2048 z 4 672 z 3 -1 429 z 2 368 z -384 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 -1 -1 2 256 z 4 156 z 3 -1 63 z 2 40 z -192 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 3 2 -1 -1 2048 z 4 672 z 3 -1 429 z 2 368 z -384 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 -1 [/itex]

 Rule Form

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

 2007-05-02