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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ah93.01

 Input Form

 Hypergeometric2F1[-(1/2), 13/4, 2, z] == (2 Sqrt[2] (2 (1 + Sqrt[1 - z]) (1 - z)^(1/4) (10 - 217 z + 231 z^2) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (10 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) - (87 + 217 (1 - z)^(1/4) + 217 Sqrt[1 - z] + 217 (1 - z)^(3/4)) z + 77 (1 + 3 (1 - z)^(1/4) + 3 Sqrt[1 - z] + 3 (1 - z)^(3/4)) z^2) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (135 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z) z)

 Standard Form

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 MathML Form

 2 F 1 ( - 1 2 , 13 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["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["13", "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["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 135 π 1 - z + 1 ( z - 1 ) z ( 2 2 ( 2 ( 1 - z + 1 ) 1 - z 4 ( 231 z 2 - 217 z + 10 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 77 ( 3 ( 1 - z ) 3 / 4 + 3 1 - z + 3 1 - z 4 + 1 ) z 2 - ( 217 ( 1 - z ) 3 / 4 + 217 1 - z + 217 1 - z 4 + 87 ) z + 10 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) HypergeometricPFQ -1 1 2 13 4 2 z 1 135 1 -1 z 1 2 1 1 2 z -1 z -1 2 2 1 2 2 1 -1 z 1 2 1 1 -1 z 1 4 231 z 2 -1 217 z 10 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 77 3 1 -1 z 3 4 3 1 -1 z 1 2 3 1 -1 z 1 4 1 z 2 -1 217 1 -1 z 3 4 217 1 -1 z 1 2 217 1 -1 z 1 4 87 z 10 1 -1 z 3 4 1 -1 z 1 2 1 -1 z 1 4 1 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 [/itex]

 Rule Form

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

 2007-05-02