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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.amy2.01

 Input Form

 HypergeometricPFQ[{1/2, 1, 1}, {3/2, 7/2}, z] == (5 I (-24 I + 68 I z + 9 Pi^2 z^(3/2)))/(96 z^2) + (5 Sqrt[1 - z] (-2 + 5 z) ArcSin[Sqrt[z]])/(8 z^(5/2)) - (5 Sqrt[1 - z] Log[1 - E^(I ArcSin[Sqrt[z]])])/(12 (-1 + z)) + (5 Sqrt[1 - z] Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))])/(12 (-1 + z)) + (15 ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))])/(8 Sqrt[z]) + (5 Sqrt[1 - z] Log[1 + E^(I ArcSin[Sqrt[z]])])/(12 (-1 + z)) + (15 I PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/(8 Sqrt[z]) - (15 I PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(8 Sqrt[z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["5", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "24"]], " ", "\[ImaginaryI]"]], "+", RowBox[List["68", " ", "\[ImaginaryI]", " ", "z"]], "+", RowBox[List["9", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], ")"]]]], RowBox[List["96", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["5", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["5", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["12", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]]], "+", FractionBox[RowBox[List["5", " ", 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["12", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]]], "+", FractionBox[RowBox[List["15", " ", 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["8", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["5", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["12", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]]], "+", FractionBox[RowBox[List["15", " ", "\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"]]]], "-", FractionBox[RowBox[List["15", " ", "\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"]]]]]]]]]]

 MathML Form

 3 F 2 ( 1 2 , 1 , 1 ; 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["1", 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 + 68 z - 24 ) 96 z 2 + 5 1 - z ( 5 z - 2 ) sin - 1 ( z ) 8 z 5 / 2 - 5 1 - z log ( 1 - sin - 1 ( z ) ) 12 ( z - 1 ) + 15 sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 8 z + 5 1 - z log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 12 ( z - 1 ) + 5 1 - z log ( 1 + sin - 1 ( z ) ) 12 ( z - 1 ) + 15 Li PolyLog 2 ( - sin - 1 ( z ) ) 8 z - 15 Li PolyLog 2 ( sin - 1 ( z ) ) 8 z HypergeometricPFQ 1 2 1 1 3 2 7 2 z 5 9 2 z 3 2 68 z -1 24 96 z 2 -1 5 1 -1 z 1 2 5 z -2 z 1 2 8 z 5 2 -1 -1 5 1 -1 z 1 2 1 -1 z 1 2 12 z -1 -1 15 z 1 2 1 -1 z 1 2 1 z 1 2 -1 8 z 1 2 -1 5 1 -1 z 1 2 1 -1 z 1 2 1 z 1 2 -1 12 z -1 -1 5 1 -1 z 1 2 1 z 1 2 12 z -1 -1 15 PolyLog 2 -1 z 1 2 8 z 1 2 -1 -1 15 PolyLog 2 z 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