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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.an3w.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", "2"]]], RowBox[List["8", " ", SqrtBox["z"]]]], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]]], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], RowBox[List["2", " ", SqrtBox["z"]]]], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]], RowBox[List["2", " ", SqrtBox["z"]]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["2", " ", SqrtBox["z"]]]]]]]]]]

 MathML Form

 3 F 2 ( 1 2 , 1 , 2 ; 3 2 , 3 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["3", "2"], 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["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) sin - 1 ( z ) 2 z - 1 - z sin - 1 ( z ) 2 ( z - 1 ) z + 1 - z log ( 1 - sin - 1 ( z ) ) 2 ( z - 1 ) - 1 - z log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 2 ( z - 1 ) - 1 - z log ( 1 + sin - 1 ( z ) ) 2 ( z - 1 ) + Li PolyLog 2 ( - sin - 1 ( z ) ) 2 z - Li PolyLog 2 ( sin - 1 ( z ) ) 2 z + π 2 8 z HypergeometricPFQ 1 2 1 2 3 2 3 2 z 1 -1 z 1 2 1 z 1 2 -1 z 1 2 2 z 1 2 -1 -1 1 -1 z 1 2 z 1 2 2 z -1 z 1 2 -1 1 -1 z 1 2 1 -1 z 1 2 2 z -1 -1 -1 1 -1 z 1 2 1 -1 z 1 2 1 z 1 2 -1 2 z -1 -1 -1 1 -1 z 1 2 1 z 1 2 2 z -1 -1 PolyLog 2 -1 z 1 2 2 z 1 2 -1 -1 PolyLog 2 z 1 2 2 z 1 2 -1 2 8 z 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02