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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.an41.01

 Input Form

 HypergeometricPFQ[{1/2, 1, 2}, {3/2, 5/2}, -z] == (3 (-4 + Pi^2 Sqrt[z]))/(16 z) + (3 Log[1 + Sqrt[z] - Sqrt[1 + z]])/ (4 Sqrt[1 + z]) - (3 Log[1 - Sqrt[z] + Sqrt[1 + z]])/(4 Sqrt[1 + z]) + (3 Sqrt[1 + z] Log[Sqrt[z] + Sqrt[1 + z]])/(4 z^(3/2)) - (3 Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (4 Sqrt[1 + z]) + (3 Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (4 Sqrt[z]) + (3 PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(4 Sqrt[z]) - (3 PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/(4 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["5", "2"]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SqrtBox["z"]]]]], ")"]]]], RowBox[List["16", " ", "z"]]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"], "-", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["4", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "-", FractionBox[RowBox[List["3", " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["4", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "+", FractionBox[RowBox[List["3", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], "-", FractionBox[RowBox[List["3", " ", 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["4", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "+", 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["4", " ", 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["4", " ", 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["4", " ", SqrtBox["z"]]]]]]]]]]

 MathML Form

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

 Rule Form

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

 2007-05-02