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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.an9w.01

 Input Form

 HypergeometricPFQ[{1/2, 1, 3}, {3/2, 5/2}, z] == (3 I (-4 I + 3 Pi^2 Sqrt[z]))/(64 z) - (3 Sqrt[1 - z] (-1 + 3 z) ArcSin[Sqrt[z]])/(16 (-1 + z) z^(3/2)) + (Sqrt[1 - z] Log[1 - E^(I ArcSin[Sqrt[z]])])/(16 (-1 + z)^2) - (Sqrt[1 - z] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (16 (-1 + z)^2) + (9 ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (16 Sqrt[z]) - (Sqrt[1 - z] Log[1 + E^(I ArcSin[Sqrt[z]])])/ (16 (-1 + z)^2) + (9 I PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/(16 Sqrt[z]) - (9 I PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(16 Sqrt[z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["5", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"], " ", SqrtBox["z"]]]]], ")"]]]], RowBox[List["64", " ", "z"]]], "-", FractionBox[RowBox[List["3", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["3", " ", "z"]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], RowBox[List["16", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], "+", 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["16", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"]]]], "-", 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["16", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["9", " ", 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["16", " ", 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["16", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["9", " ", "\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]], RowBox[List["16", " ", SqrtBox["z"]]]], "-", FractionBox[RowBox[List["9", " ", "\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["16", " ", SqrtBox["z"]]]]]]]]]]

 MathML Form

 3 F 2 ( 1 2 , 1 , 3 ; 3 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["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["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] 3 ( 3 π 2 z - 4 ) 64 z - 3 1 - z ( 3 z - 1 ) sin - 1 ( z ) 16 ( z - 1 ) z 3 / 2 + 1 - z log ( 1 - sin - 1 ( z ) ) 16 ( z - 1 ) 2 + 9 sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 16 z - 1 - z log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 16 ( z - 1 ) 2 - 1 - z log ( 1 + sin - 1 ( z ) ) 16 ( z - 1 ) 2 + 9 Li PolyLog 2 ( - sin - 1 ( z ) ) 16 z - 9 Li PolyLog 2 ( sin - 1 ( z ) ) 16 z HypergeometricPFQ 1 2 1 3 3 2 5 2 z 3 3 2 z 1 2 -1 4 64 z -1 -1 3 1 -1 z 1 2 3 z -1 z 1 2 16 z -1 z 3 2 -1 1 -1 z 1 2 1 -1 z 1 2 16 z -1 2 -1 9 z 1 2 1 -1 z 1 2 1 z 1 2 -1 16 z 1 2 -1 -1 1 -1 z 1 2 1 -1 z 1 2 1 z 1 2 -1 16 z -1 2 -1 -1 1 -1 z 1 2 1 z 1 2 16 z -1 2 -1 9 PolyLog 2 -1 z 1 2 16 z 1 2 -1 -1 9 PolyLog 2 z 1 2 16 z 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02