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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.2351.01

 Input Form

 HypergeometricPFQ[{-(7/2), -(5/2), -(5/2)}, {3/2, 3/2}, z] == (Sqrt[1 - z] (2115171 - 15487702 z + 4150936 z^2 - 3600 z^3))/2359296 + (175 (5 Pi^2 - 360 Pi^2 z + 720 Pi^2 z^2 - 64 Pi^2 z^3))/ (393216 Sqrt[-z]) - (35 (-1725 + 18000 z + 93600 z^2 - 22016 z^3) Log[Sqrt[1 - z] + Sqrt[-z]])/(786432 Sqrt[-z]) - (175 (5 - 360 z + 720 z^2 - 64 z^3) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/ (65536 Sqrt[-z]) + (175 (5 - 360 z + 720 z^2 - 64 z^3) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/ (32768 Sqrt[-z]) + (175 (5 - 360 z + 720 z^2 - 64 z^3) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/(32768 Sqrt[-z]) - (175 (5 - 360 z + 720 z^2 - 64 z^3) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/ (32768 Sqrt[-z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["2115171", "-", RowBox[List["15487702", " ", "z"]], "+", RowBox[List["4150936", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3600", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], "2359296"], "+", FractionBox[RowBox[List["175", " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox["\[Pi]", "2"]]], "-", RowBox[List["360", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]], "+", RowBox[List["720", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["64", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "3"]]]]], ")"]]]], RowBox[List["393216", " ", SqrtBox[RowBox[List["-", "z"]]]]]], "-", FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1725"]], "+", RowBox[List["18000", " ", "z"]], "+", RowBox[List["93600", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["22016", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["786432", " ", SqrtBox[RowBox[List["-", "z"]]]]]], "-", FractionBox[RowBox[List["175", " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["360", " ", "z"]], "+", RowBox[List["720", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], "2"]]], RowBox[List["65536", " ", SqrtBox[RowBox[List["-", "z"]]]]]], "+", FractionBox[RowBox[List["175", " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["360", " ", "z"]], "+", RowBox[List["720", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["32768", " ", SqrtBox[RowBox[List["-", "z"]]]]]], "+", FractionBox[RowBox[List["175", " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["360", " ", "z"]], "+", RowBox[List["720", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", "z"]]]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["32768", " ", SqrtBox[RowBox[List["-", "z"]]]]]], "-", FractionBox[RowBox[List["175", " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["360", " ", "z"]], "+", RowBox[List["720", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["32768", " ", SqrtBox[RowBox[List["-", "z"]]]]]]]]]]]]

 MathML Form

 3 F 2 ( - 7 2 , - 5 2 , - 5 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[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["5", "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] - 175 ( - 64 z 3 + 720 z 2 - 360 z + 5 ) log 2 ( 1 - z + - z ) 65536 - z - 35 ( - 22016 z 3 + 93600 z 2 + 18000 z - 1725 ) log ( 1 - z + - z ) 786432 - z + 175 ( - 64 z 3 + 720 z 2 - 360 z + 5 ) log ( 1 - z + - z + 1 ) log ( 1 - z + - z ) 32768 - z + 1 - z ( - 3600 z 3 + 4150936 z 2 - 15487702 z + 2115171 ) 2359296 + 175 ( - 64 π 2 z 3 + 720 π 2 z 2 - 360 π 2 z + 5 π 2 ) 393216 - z + 175 ( - 64 z 3 + 720 z 2 - 360 z + 5 ) Li PolyLog 2 ( - 1 - z - - z ) 32768 - z - 175 ( - 64 z 3 + 720 z 2 - 360 z + 5 ) Li PolyLog 2 ( - 1 - z - - z + 1 ) 32768 - z HypergeometricPFQ -1 7 2 -1 5 2 -1 5 2 3 2 3 2 z -1 175 -64 z 3 720 z 2 -1 360 z 5 1 -1 z 1 2 -1 z 1 2 2 65536 -1 z 1 2 -1 -1 35 -22016 z 3 93600 z 2 18000 z -1725 1 -1 z 1 2 -1 z 1 2 786432 -1 z 1 2 -1 175 -64 z 3 720 z 2 -1 360 z 5 1 -1 z 1 2 -1 z 1 2 1 1 -1 z 1 2 -1 z 1 2 32768 -1 z 1 2 -1 1 -1 z 1 2 -3600 z 3 4150936 z 2 -1 15487702 z 2115171 2359296 -1 175 -64 2 z 3 720 2 z 2 -1 360 2 z 5 2 393216 -1 z 1 2 -1 175 -64 z 3 720 z 2 -1 360 z 5 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 32768 -1 z 1 2 -1 -1 175 -64 z 3 720 z 2 -1 360 z 5 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 1 32768 -1 z 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02