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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.an4e.01

 Input Form

 HypergeometricPFQ[{1/2, 1, 2}, {5/2, 5/2}, z] == (9 I (-2 Pi^2 - 12 I Sqrt[z] + Pi^2 z))/(32 z^(3/2)) - (9 Sqrt[1 - z] ArcSin[Sqrt[z]])/(8 z^(3/2)) - (9 Sqrt[1 - z] (2 - 7 z + 3 z^2) Log[1 - E^(I ArcSin[Sqrt[z]])])/ (8 (-1 + z)^2 z) + (9 Sqrt[1 - z] (2 - 7 z + 3 z^2) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (8 (-1 + z)^2 z) + (9 (-2 + z) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (8 z^(3/2)) + (9 Sqrt[1 - z] (2 - 7 z + 3 z^2) Log[1 + E^(I ArcSin[Sqrt[z]])])/(8 (-1 + z)^2 z) + (9 I (-2 + z) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/(8 z^(3/2)) - (9 I (-2 + z) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(8 z^(3/2))

 Standard Form

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 MathML Form

 3 F 2 ( 1 2 , 1 , 2 ; 5 2 , 5 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["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", 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["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "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] 9 ( π 2 z - 12 z - 2 π 2 ) 32 z 3 / 2 - 9 1 - z sin - 1 ( z ) 8 z 3 / 2 - 9 1 - z ( 3 z 2 - 7 z + 2 ) log ( 1 - sin - 1 ( z ) ) 8 ( z - 1 ) 2 z + 9 1 - z ( 3 z 2 - 7 z + 2 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 8 ( z - 1 ) 2 z + 9 ( z - 2 ) sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 8 z 3 / 2 + 9 1 - z ( 3 z 2 - 7 z + 2 ) log ( 1 + sin - 1 ( z ) ) 8 ( z - 1 ) 2 z + 9 ( z - 2 ) Li PolyLog 2 ( - sin - 1 ( z ) ) 8 z 3 / 2 - 9 ( z - 2 ) Li PolyLog 2 ( sin - 1 ( z ) ) 8 z 3 / 2 HypergeometricPFQ 1 2 1 2 5 2 5 2 z 9 2 z -1 12 z 1 2 -1 2 2 32 z 3 2 -1 -1 9 1 -1 z 1 2 z 1 2 8 z 3 2 -1 -1 9 1 -1 z 1 2 3 z 2 -1 7 z 2 1 -1 z 1 2 8 z -1 2 z -1 9 1 -1 z 1 2 3 z 2 -1 7 z 2 1 -1 z 1 2 1 z 1 2 -1 8 z -1 2 z -1 9 z -2 z 1 2 1 -1 z 1 2 1 z 1 2 -1 8 z 3 2 -1 9 1 -1 z 1 2 3 z 2 -1 7 z 2 1 z 1 2 8 z -1 2 z -1 9 z -2 PolyLog 2 -1 z 1 2 8 z 3 2 -1 -1 9 z -2 PolyLog 2 z 1 2 8 z 3 2 -1 [/itex]

 Rule Form

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

 2007-05-02