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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.af7w.01

 Input Form

 Hypergeometric2F1[-(7/4), 13/4, 17/4, z] == (1/(327680 z^(13/4))) (13 (-8 (1 - z)^(3/4) z^(1/4) (315 + 252 z + 224 z^2 - 2944 z^3 + 2048 z^4) - 630 Sqrt[2] ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 630 Sqrt[2] ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 315 Sqrt[2] Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 315 Sqrt[2] Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))

 Standard Form

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 MathML Form

 2 F 1 ( - 7 4 , 13 4 ; 17 4 ; 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["7", "4"]]], 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[FractionBox["17", "4"], 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 327680 z 13 / 4 ( 13 ( - 8 ( 1 - z ) 3 / 4 z 4 ( 2048 z 4 - 2944 z 3 + 224 z 2 + 252 z + 315 ) - 630 2 tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) - 630 2 tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) - 315 2 log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) + 315 2 log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ) ) HypergeometricPFQ -1 7 4 13 4 17 4 z 1 327680 z 13 4 -1 13 -8 1 -1 z 3 4 z 1 4 2048 z 4 -1 2944 z 3 224 z 2 252 z 315 -1 630 2 1 2 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 630 2 1 2 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 315 2 1 2 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 315 2 1 2 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 [/itex]

 Rule Form

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

 2007-05-02