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/07.27.03.1749.01

 Input Form

 HypergeometricPFQ[{-(7/2), -(7/2), 2}, {3/2, 7/2}, z] == (-735 + 8575 z + 2413521 z^2 + 8311723 z^3 + 4840220 z^4 + 417480 z^5)/ (3145728 z^2) + (245 (-1 + 12 z - 700 z^2 - 3600 z^3 + 825 z^4 + 3076 z^5 + 388 z^6) Log[1 - Sqrt[z]])/(2097152 z^(5/2)) - (245 (-1 + 12 z - 700 z^2 - 3600 z^3 + 825 z^4 + 3076 z^5 + 388 z^6) Log[1 + Sqrt[z]])/(2097152 z^(5/2)) - (3675 (5 + 80 z + 150 z^2 + 56 z^3 + 3 z^4) PolyLog[2, -Sqrt[z]])/ (524288 Sqrt[z]) + (3675 (5 + 80 z + 150 z^2 + 56 z^3 + 3 z^4) PolyLog[2, Sqrt[z]])/(524288 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["7", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "735"]], "+", RowBox[List["8575", " ", "z"]], "+", RowBox[List["2413521", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8311723", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4840220", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["417480", " ", SuperscriptBox["z", "5"]]]]], RowBox[List["3145728", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["245", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["12", " ", "z"]], "-", RowBox[List["700", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["825", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3076", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["388", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["2097152", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["245", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["12", " ", "z"]], "-", RowBox[List["700", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["825", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3076", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["388", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["2097152", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["150", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["56", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["524288", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["150", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["56", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["524288", " ", SqrtBox["z"]]]]]]]]]]

 MathML Form

 3 F 2 ( - 7 2 , - 7 2 , 2 ; 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[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["7", "2"]]], 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["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] 417480 z 5 + 4840220 z 4 + 8311723 z 3 + 2413521 z 2 + 8575 z - 735 3145728 z 2 + 245 ( 388 z 6 + 3076 z 5 + 825 z 4 - 3600 z 3 - 700 z 2 + 12 z - 1 ) log ( 1 - z ) 2097152 z 5 / 2 - 245 ( 388 z 6 + 3076 z 5 + 825 z 4 - 3600 z 3 - 700 z 2 + 12 z - 1 ) log ( z + 1 ) 2097152 z 5 / 2 - 3675 ( 3 z 4 + 56 z 3 + 150 z 2 + 80 z + 5 ) Li PolyLog 2 ( - z ) 524288 z + 3675 ( 3 z 4 + 56 z 3 + 150 z 2 + 80 z + 5 ) Li PolyLog 2 ( z ) 524288 z HypergeometricPFQ -1 7 2 -1 7 2 2 3 2 7 2 z 417480 z 5 4840220 z 4 8311723 z 3 2413521 z 2 8575 z -735 3145728 z 2 -1 245 388 z 6 3076 z 5 825 z 4 -1 3600 z 3 -1 700 z 2 12 z -1 1 -1 z 1 2 2097152 z 5 2 -1 -1 245 388 z 6 3076 z 5 825 z 4 -1 3600 z 3 -1 700 z 2 12 z -1 z 1 2 1 2097152 z 5 2 -1 -1 3675 3 z 4 56 z 3 150 z 2 80 z 5 PolyLog 2 -1 z 1 2 524288 z 1 2 -1 3675 3 z 4 56 z 3 150 z 2 80 z 5 PolyLog 2 z 1 2 524288 z 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "735"]], "+", RowBox[List["8575", " ", "z"]], "+", RowBox[List["2413521", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8311723", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4840220", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["417480", " ", SuperscriptBox["z", "5"]]]]], RowBox[List["3145728", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["245", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["12", " ", "z"]], "-", RowBox[List["700", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["825", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3076", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["388", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["2097152", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["245", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["12", " ", "z"]], "-", RowBox[List["700", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["825", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3076", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["388", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["2097152", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["150", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["56", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["524288", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["80", " ", "z"]], "+", RowBox[List["150", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["56", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["524288", " ", SqrtBox["z"]]]]]]]]]]

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

 2007-05-02