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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ak8u.01

 Input Form

 Hypergeometric2F1[3/2, 11/4, 6, z] == (1/(2205 Pi Sqrt[1 + Sqrt[1 - z]] z^5)) (1024 Sqrt[2] (2 (1 + Sqrt[1 - z]) (-1024 + 1888 z - 858 z^2 + 15 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1024 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) - 32 (59 + 59 (1 - z)^(1/4) + 59 Sqrt[1 - z] + 43 (1 - z)^(3/4)) z + 66 (13 + 13 (1 - z)^(1/4) + 13 Sqrt[1 - z] + 5 (1 - z)^(3/4)) z^2 + 15 (-1 - (1 - z)^(1/4) - Sqrt[1 - z] + (1 - z)^(3/4)) z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))

 Standard Form

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 MathML Form

 2 F 1 ( 3 2 , 11 4 ; 6 ; 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", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["6", 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 2205 π 1 - z + 1 z 5 ( 1024 2 ( 2 ( 1 - z + 1 ) ( 15 z 3 - 858 z 2 + 1888 z - 1024 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 15 ( ( 1 - z ) 3 / 4 - 1 - z - 1 - z 4 - 1 ) z 3 + 66 ( 5 ( 1 - z ) 3 / 4 + 13 1 - z + 13 1 - z 4 + 13 ) z 2 - 32 ( 43 ( 1 - z ) 3 / 4 + 59 1 - z + 59 1 - z 4 + 59 ) z + 1024 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ 3 2 11 4 6 z 1 2205 1 -1 z 1 2 1 1 2 z 5 -1 1024 2 1 2 2 1 -1 z 1 2 1 15 z 3 -1 858 z 2 1888 z -1024 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 15 1 -1 z 3 4 -1 1 -1 z 1 2 -1 1 -1 z 1 4 -1 z 3 66 5 1 -1 z 3 4 13 1 -1 z 1 2 13 1 -1 z 1 4 13 z 2 -1 32 43 1 -1 z 3 4 59 1 -1 z 1 2 59 1 -1 z 1 4 59 z 1024 1 -1 z 3 4 1 -1 z 1 2 1 -1 z 1 4 1 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02