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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.auqj.01

 Input Form

 HypergeometricPFQ[{5/2, 4, 4}, {7/2, 7/2}, z] == (25 (-3 I Pi^2 + 20 Sqrt[z] + 9 I Pi^2 z - 68 z^(3/2) - 9 I Pi^2 z^2 - 12 z^(5/2) + 3 I Pi^2 z^3))/(3072 (-1 + z)^3 z^(5/2)) - (25 Sqrt[1 - z] (-2 + 10 z - 26 z^2 + 3 z^3) ArcSin[Sqrt[z]])/ (768 (-1 + z)^4 z^(5/2)) + (25 Sqrt[1 - z] (3 - 10 z - 10 z^2 + 2 z^3) Log[1 - E^(I ArcSin[Sqrt[z]])])/(768 (-1 + z)^4 z^2) - (25 Sqrt[1 - z] (3 - 10 z - 10 z^2 + 2 z^3) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (768 (-1 + z)^4 z^2) + (25 ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))])/(256 z^(5/2)) - (25 Sqrt[1 - z] (3 - 10 z - 10 z^2 + 2 z^3) Log[1 + E^(I ArcSin[Sqrt[z]])])/ (768 (-1 + z)^4 z^2) + (25 I PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/ (256 z^(5/2)) - (25 I PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(256 z^(5/2))

 Standard Form

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 MathML Form

 3 F 2 ( 5 2 , 4 , 4 ; 7 2 , 7 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], 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] 25 ( 3 π 2 z 3 - 12 z 5 / 2 - 9 π 2 z 2 - 68 z 3 / 2 + 9 π 2 z + 20 z - 3 π 2 ) 3072 ( z - 1 ) 3 z 5 / 2 - 25 1 - z ( 3 z 3 - 26 z 2 + 10 z - 2 ) sin - 1 ( z ) 768 ( z - 1 ) 4 z 5 / 2 + 25 1 - z ( 2 z 3 - 10 z 2 - 10 z + 3 ) log ( 1 - sin - 1 ( z ) ) 768 ( z - 1 ) 4 z 2 - 25 1 - z ( 2 z 3 - 10 z 2 - 10 z + 3 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 768 ( z - 1 ) 4 z 2 + 25 sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 256 z 5 / 2 - 25 1 - z ( 2 z 3 - 10 z 2 - 10 z + 3 ) log ( 1 + sin - 1 ( z ) ) 768 ( z - 1 ) 4 z 2 + 25 Li PolyLog 2 ( - sin - 1 ( z ) ) 256 z 5 / 2 - 25 Li PolyLog 2 ( sin - 1 ( z ) ) 256 z 5 / 2 HypergeometricPFQ 5 2 4 4 7 2 7 2 z 25 3 2 z 3 -1 12 z 5 2 -1 9 2 z 2 -1 68 z 3 2 9 2 z 20 z 1 2 -1 3 2 3072 z -1 3 z 5 2 -1 -1 25 1 -1 z 1 2 3 z 3 -1 26 z 2 10 z -2 z 1 2 768 z -1 4 z 5 2 -1 25 1 -1 z 1 2 2 z 3 -1 10 z 2 -1 10 z 3 1 -1 z 1 2 768 z -1 4 z 2 -1 -1 25 1 -1 z 1 2 2 z 3 -1 10 z 2 -1 10 z 3 1 -1 z 1 2 1 z 1 2 -1 768 z -1 4 z 2 -1 25 z 1 2 1 -1 z 1 2 1 z 1 2 -1 256 z 5 2 -1 -1 25 1 -1 z 1 2 2 z 3 -1 10 z 2 -1 10 z 3 1 z 1 2 768 z -1 4 z 2 -1 25 PolyLog 2 -1 z 1 2 256 z 5 2 -1 -1 25 PolyLog 2 z 1 2 256 z 5 2 -1 [/itex]

 Rule Form

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

 2007-05-02