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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.ana0.01

 Input Form

 HypergeometricPFQ[{1/2, 1, 3}, {3/2, 7/2}, z] == (5 I (-24 I - 28 I z + 9 Pi^2 z^(3/2)))/(256 z^2) - (15 Sqrt[1 - z] (2 + 3 z) ArcSin[Sqrt[z]])/(64 z^(5/2)) - (5 Sqrt[1 - z] (9 - 13 z + 6 z^2) Log[1 - E^(I ArcSin[Sqrt[z]])])/ (64 (-1 + z)^3) + (5 Sqrt[1 - z] (9 - 13 z + 6 z^2) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (64 (-1 + z)^3) + (45 ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (64 Sqrt[z]) + (5 Sqrt[1 - z] (9 - 13 z + 6 z^2) Log[1 + E^(I ArcSin[Sqrt[z]])])/(64 (-1 + z)^3) + (45 I PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/(64 Sqrt[z]) - (45 I PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(64 Sqrt[z])

 Standard Form

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 MathML Form

 3 F 2 ( 1 2 , 1 , 3 ; 3 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["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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["3", "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] 5 ( 9 π 2 z 3 / 2 - 28 z - 24 ) 256 z 2 - 15 1 - z ( 3 z + 2 ) sin - 1 ( z ) 64 z 5 / 2 - 5 1 - z ( 6 z 2 - 13 z + 9 ) log ( 1 - sin - 1 ( z ) ) 64 ( z - 1 ) 3 + 5 1 - z ( 6 z 2 - 13 z + 9 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 64 ( z - 1 ) 3 + 45 sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 64 z + 5 1 - z ( 6 z 2 - 13 z + 9 ) log ( 1 + sin - 1 ( z ) ) 64 ( z - 1 ) 3 + 45 Li PolyLog 2 ( - sin - 1 ( z ) ) 64 z - 45 Li PolyLog 2 ( sin - 1 ( z ) ) 64 z HypergeometricPFQ 1 2 1 3 3 2 7 2 z 5 9 2 z 3 2 -1 28 z -1 24 256 z 2 -1 -1 15 1 -1 z 1 2 3 z 2 z 1 2 64 z 5 2 -1 -1 5 1 -1 z 1 2 6 z 2 -1 13 z 9 1 -1 z 1 2 64 z -1 3 -1 5 1 -1 z 1 2 6 z 2 -1 13 z 9 1 -1 z 1 2 1 z 1 2 -1 64 z -1 3 -1 45 z 1 2 1 -1 z 1 2 1 z 1 2 -1 64 z 1 2 -1 5 1 -1 z 1 2 6 z 2 -1 13 z 9 1 z 1 2 64 z -1 3 -1 45 PolyLog 2 -1 z 1 2 64 z 1 2 -1 -1 45 PolyLog 2 z 1 2 64 z 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02