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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.aim5.01

 Input Form

 Hypergeometric2F1[1/2, 3/4, 5, z] == (1/(20475 Pi Sqrt[1 + Sqrt[1 - z]] z^4)) (256 Sqrt[2] (2 (1 + Sqrt[1 - z]) (-384 + 1408 z - 1888 z^2 + 1095 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (384 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) - 64 (22 + 22 (1 - z)^(1/4) + 22 Sqrt[1 - z] + 19 (1 - z)^(3/4)) z + 4 (472 + 472 (1 - z)^(1/4) + 472 Sqrt[1 - z] + 335 (1 - z)^(3/4)) z^2 - 15 (73 + 73 (1 - z)^(1/4) + 73 Sqrt[1 - z] + 39 (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 ( 1 2 , 3 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["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "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["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 20475 π 1 - z + 1 z 4 ( 256 2 ( 2 ( 1 - z + 1 ) ( 1095 z 3 - 1888 z 2 + 1408 z - 384 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( - 15 ( 39 ( 1 - z ) 3 / 4 + 73 1 - z + 73 1 - z 4 + 73 ) z 3 + 4 ( 335 ( 1 - z ) 3 / 4 + 472 1 - z + 472 1 - z 4 + 472 ) z 2 - 64 ( 19 ( 1 - z ) 3 / 4 + 22 1 - z + 22 1 - z 4 + 22 ) z + 384 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ 1 2 3 4 5 z 1 20475 1 -1 z 1 2 1 1 2 z 4 -1 256 2 1 2 2 1 -1 z 1 2 1 1095 z 3 -1 1888 z 2 1408 z -384 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -15 39 1 -1 z 3 4 73 1 -1 z 1 2 73 1 -1 z 1 4 73 z 3 4 335 1 -1 z 3 4 472 1 -1 z 1 2 472 1 -1 z 1 4 472 z 2 -1 64 19 1 -1 z 3 4 22 1 -1 z 1 2 22 1 -1 z 1 4 22 z 384 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