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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ak7k.01

 Input Form

 Hypergeometric2F1[3/2, 7/4, 6, z] == (1/(4095 Pi Sqrt[1 + Sqrt[1 - z]] z^5)) (1024 Sqrt[2] (-2 (1 + Sqrt[1 - z]) (-1024 + 2784 z - 2426 z^2 + 645 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 (87 + 87 (1 - z)^(1/4) + 87 Sqrt[1 - z] + 71 (1 - z)^(3/4)) z - 2 (1213 + 1213 (1 - z)^(1/4) + 1213 Sqrt[1 - z] + 725 (1 - z)^(3/4)) z^2 + 15 (43 + 43 (1 - z)^(1/4) + 43 Sqrt[1 - z] + 13 (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 , 7 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["7", "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 4095 π 1 - z + 1 z 5 ( 1024 2 ( ( 15 ( 13 ( 1 - z ) 3 / 4 + 43 1 - z + 43 1 - z 4 + 43 ) z 3 - 2 ( 725 ( 1 - z ) 3 / 4 + 1213 1 - z + 1213 1 - z 4 + 1213 ) z 2 + 32 ( 71 ( 1 - z ) 3 / 4 + 87 1 - z + 87 1 - z 4 + 87 ) z - 1024 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - 2 ( 1 - z + 1 ) ( 645 z 3 - 2426 z 2 + 2784 z - 1024 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ 3 2 7 4 6 z 1 4095 1 -1 z 1 2 1 1 2 z 5 -1 1024 2 1 2 15 13 1 -1 z 3 4 43 1 -1 z 1 2 43 1 -1 z 1 4 43 z 3 -1 2 725 1 -1 z 3 4 1213 1 -1 z 1 2 1213 1 -1 z 1 4 1213 z 2 32 71 1 -1 z 3 4 87 1 -1 z 1 2 87 1 -1 z 1 4 87 z -1 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 -1 2 1 -1 z 1 2 1 645 z 3 -1 2426 z 2 2784 z -1024 EllipticE 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