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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[5/4, 3/2, 5, z] == -((1/(1155 Pi Sqrt[1 + Sqrt[1 - z]] z^4)) (512 Sqrt[2] (2 (1 + Sqrt[1 - z]) (1 - z)^(1/4) (192 - 368 z + 171 z^2) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (192 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) - 16 (29 + 23 (1 - z)^(1/4) + 23 Sqrt[1 - z] + 23 (1 - z)^(3/4)) z + (337 + 171 (1 - z)^(1/4) + 171 Sqrt[1 - z] + 171 (1 - z)^(3/4)) z^2 - 60 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])))

 Standard Form

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 MathML Form

 2 F 1 ( 5 4 , 3 2 ; 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["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "2"], 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 1155 π 1 - z + 1 z 4 ( 512 2 ( 2 ( 1 - z + 1 ) 1 - z 4 ( 171 z 2 - 368 z + 192 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( - 60 z 3 + ( 171 ( 1 - z ) 3 / 4 + 171 1 - z + 171 1 - z 4 + 337 ) z 2 - 16 ( 23 ( 1 - z ) 3 / 4 + 23 1 - z + 23 1 - z 4 + 29 ) z + 192 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) HypergeometricPFQ 5 4 3 2 5 z -1 1 1155 1 -1 z 1 2 1 1 2 z 4 -1 512 2 1 2 2 1 -1 z 1 2 1 1 -1 z 1 4 171 z 2 -1 368 z 192 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 -60 z 3 171 1 -1 z 3 4 171 1 -1 z 1 2 171 1 -1 z 1 4 337 z 2 -1 16 23 1 -1 z 3 4 23 1 -1 z 1 2 23 1 -1 z 1 4 29 z 192 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