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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.an9u.01

 Input Form

 HypergeometricPFQ[{1/2, 1, 3}, {3/2, 3/2}, -z] == (3 Pi^2 + 4 Sqrt[z] + 3 Pi^2 z)/(32 Sqrt[z] (1 + z)) + ((-5 - 4 z) Log[1 + Sqrt[z] - Sqrt[1 + z]])/(8 (1 + z)^(3/2)) + ((5 + 4 z) Log[1 - Sqrt[z] + Sqrt[1 + z]])/(8 (1 + z)^(3/2)) + ((4 + 3 z) Log[Sqrt[z] + Sqrt[1 + z]])/(8 Sqrt[z] (1 + z)^(3/2)) + ((5 + 4 z) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (8 (1 + z)^(3/2)) + (3 Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (8 Sqrt[z]) + (3 PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(8 Sqrt[z]) - (3 PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/(8 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["3", "2"]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"]]], "+", RowBox[List["4", " ", SqrtBox["z"]]], "+", RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]]]], RowBox[List["32", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "-", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"], "-", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["5", "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["4", "+", RowBox[List["3", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["5", "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox["1", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"]]]], "-", FractionBox[RowBox[List["3", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox["1", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"]]]]]]]]]]

 MathML Form

 3 F 2 ( 1 2 , 1 , 3 ; 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["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["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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 π 2 z + 4 z + 3 π 2 32 z ( z + 1 ) + ( - 4 z - 5 ) log ( z - z + 1 + 1 ) 8 ( z + 1 ) 3 / 2 + ( 4 z + 5 ) log ( - z + z + 1 + 1 ) 8 ( z + 1 ) 3 / 2 + ( 3 z + 4 ) log ( z + z + 1 ) 8 z ( z + 1 ) 3 / 2 + ( 4 z + 5 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) 8 ( z + 1 ) 3 / 2 + 3 log ( z + z + 1 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) 8 z + 3 Li PolyLog 2 ( - 1 z + z + 1 ) 8 z - 3 Li PolyLog 2 ( 1 z + z + 1 ) 8 z HypergeometricPFQ 1 2 1 3 3 2 3 2 -1 z 3 2 z 4 z 1 2 3 2 32 z 1 2 z 1 -1 -4 z -5 z 1 2 -1 z 1 1 2 1 8 z 1 3 2 -1 4 z 5 -1 z 1 2 z 1 1 2 1 8 z 1 3 2 -1 3 z 4 z 1 2 z 1 1 2 8 z 1 2 z 1 3 2 -1 4 z 5 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 8 z 1 3 2 -1 3 z 1 2 z 1 1 2 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 8 z 1 2 -1 3 PolyLog 2 -1 1 z 1 2 z 1 1 2 -1 8 z 1 2 -1 -1 3 PolyLog 2 1 z 1 2 z 1 1 2 -1 8 z 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"]]], "+", RowBox[List["4", " ", SqrtBox["z"]]], "+", RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]]]], RowBox[List["32", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "-", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"], "-", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["5", "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["4", "+", RowBox[List["3", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["5", "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox["1", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"]]]], "-", FractionBox[RowBox[List["3", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox["1", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], "]"]]]], RowBox[List["8", " ", SqrtBox["z"]]]]]]]]]]

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

 2007-05-02