html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.amy3.01

 Input Form

 HypergeometricPFQ[{1/2, 1, 1}, {3/2, 7/2}, -z] == (5 (24 + 68 z + 9 Pi^2 z^(3/2)))/(96 z^2) + (5 Log[1 + Sqrt[z] - Sqrt[1 + z]])/(12 Sqrt[1 + z]) - (5 Log[1 - Sqrt[z] + Sqrt[1 + z]])/(12 Sqrt[1 + z]) - (5 Sqrt[1 + z] (2 + 5 z) Log[Sqrt[z] + Sqrt[1 + z]])/(8 z^(5/2)) - (5 Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (12 Sqrt[1 + z]) + (15 Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (8 Sqrt[z]) + (15 PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(8 Sqrt[z]) - (15 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", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List["24", "+", RowBox[List["68", " ", "z"]], "+", RowBox[List["9", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], ")"]]]], RowBox[List["96", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["5", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"], "-", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["12", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "-", FractionBox[RowBox[List["5", " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["12", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "-", FractionBox[RowBox[List["5", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["5", " ", 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["12", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "+", FractionBox[RowBox[List["15", " ", 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["15", " ", 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["15", " ", 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 , 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[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] 5 ( 9 π 2 z 3 / 2 + 68 z + 24 ) 96 z 2 + 5 log ( z - z + 1 + 1 ) 12 z + 1 - 5 log ( - z + z + 1 + 1 ) 12 z + 1 - 5 z + 1 ( 5 z + 2 ) log ( z + z + 1 ) 8 z 5 / 2 + 15 log ( z + z + 1 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) 8 z - 5 log ( z + z + 1 - 1 z + z + 1 + 1 ) 12 z + 1 + 15 Li PolyLog 2 ( - 1 z + z + 1 ) 8 z - 15 Li PolyLog 2 ( 1 z + z + 1 ) 8 z HypergeometricPFQ 1 2 1 1 3 2 7 2 -1 z 5 9 2 z 3 2 68 z 24 96 z 2 -1 5 z 1 2 -1 z 1 1 2 1 12 z 1 1 2 -1 -1 5 -1 z 1 2 z 1 1 2 1 12 z 1 1 2 -1 -1 5 z 1 1 2 5 z 2 z 1 2 z 1 1 2 8 z 5 2 -1 15 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 -1 5 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 12 z 1 1 2 -1 15 PolyLog 2 -1 1 z 1 2 z 1 1 2 -1 8 z 1 2 -1 -1 15 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", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List["24", "+", RowBox[List["68", " ", "z"]], "+", RowBox[List["9", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], ")"]]]], RowBox[List["96", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["5", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"], "-", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["12", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "-", FractionBox[RowBox[List["5", " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["12", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "-", FractionBox[RowBox[List["5", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["5", " ", 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["12", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "+", FractionBox[RowBox[List["15", " ", 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["15", " ", 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["15", " ", 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