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/07.22.03.7998.01

 Input Form

 HypergeometricPFQ[{-(23/4)}, {-(9/2), -(19/4)}, z] == (1/124428150) ((62214075 + 62214075 E^(4 Sqrt[z]) + 124428150 Sqrt[z] - 124428150 E^(4 Sqrt[z]) Sqrt[z] + 107692200 z + 107692200 E^(4 Sqrt[z]) z + 49480200 z^(3/2) - 49480200 E^(4 Sqrt[z]) z^(3/2) + 11032560 z^2 + 11032560 E^(4 Sqrt[z]) z^2 + 332640 z^(5/2) - 332640 E^(4 Sqrt[z]) z^(5/2) - 120960 z^3 - 120960 E^(4 Sqrt[z]) z^3 + 53760 z^(7/2) - 53760 E^(4 Sqrt[z]) z^(7/2) - 30720 z^4 - 30720 E^(4 Sqrt[z]) z^4 + 24576 z^(9/2) - 24576 E^(4 Sqrt[z]) z^(9/2) - 32768 z^5 - 32768 E^(4 Sqrt[z]) z^5 + 131072 z^(11/2) - 131072 E^(4 Sqrt[z]) z^(11/2) + 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) Erf[Sqrt[2] z^(1/4)] + 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["23", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["19", "4"]]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "124428150"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["62214075", "+", RowBox[List["62214075", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]]]], "+", RowBox[List["124428150", " ", SqrtBox["z"]]], "-", RowBox[List["124428150", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SqrtBox["z"]]], "+", RowBox[List["107692200", " ", "z"]], "+", RowBox[List["107692200", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", "z"]], "+", RowBox[List["49480200", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["49480200", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["11032560", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["11032560", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["332640", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["332640", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["120960", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["120960", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["53760", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["53760", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["30720", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["30720", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["24576", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["24576", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["32768", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["32768", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["131072", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["131072", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["23", "/", "4"]]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List["131072", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["23", "/", "4"]]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 1 F 2 ( - 23 4 ; - 9 2 , - 19 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["23", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["9", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["19", "4"]]], 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] 1 124428150 ( - 2 z ( 131072 2 z 2 π erf ( 2 z 4 ) z 23 / 4 + 131072 2 z 2 π erfi ( 2 z 4 ) z 23 / 4 - 131072 4 z z 11 / 2 + 131072 z 11 / 2 - 32768 4 z z 5 - 32768 z 5 - 24576 4 z z 9 / 2 + 24576 z 9 / 2 - 30720 4 z z 4 - 30720 z 4 - 53760 4 z z 7 / 2 + 53760 z 7 / 2 - 120960 4 z z 3 - 120960 z 3 - 332640 4 z z 5 / 2 + 332640 z 5 / 2 + 11032560 4 z z 2 + 11032560 z 2 - 49480200 4 z z 3 / 2 + 49480200 z 3 / 2 + 107692200 4 z z + 107692200 z - 124428150 4 z z + 124428150 z + 62214075 4 z + 62214075 ) ) HypergeometricPFQ -1 23 4 -1 9 2 -1 19 4 z 1 124428150 -2 z 1 2 131072 2 z 1 2 2 1 2 Erf 2 1 2 z 1 4 z 23 4 131072 2 z 1 2 2 1 2 Erfi 2 1 2 z 1 4 z 23 4 -1 131072 4 z 1 2 z 11 2 131072 z 11 2 -1 32768 4 z 1 2 z 5 -1 32768 z 5 -1 24576 4 z 1 2 z 9 2 24576 z 9 2 -1 30720 4 z 1 2 z 4 -1 30720 z 4 -1 53760 4 z 1 2 z 7 2 53760 z 7 2 -1 120960 4 z 1 2 z 3 -1 120960 z 3 -1 332640 4 z 1 2 z 5 2 332640 z 5 2 11032560 4 z 1 2 z 2 11032560 z 2 -1 49480200 4 z 1 2 z 3 2 49480200 z 3 2 107692200 4 z 1 2 z 107692200 z -1 124428150 4 z 1 2 z 1 2 124428150 z 1 2 62214075 4 z 1 2 62214075 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["23", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", FractionBox["19", "4"]]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["62214075", "+", RowBox[List["62214075", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]]]], "+", RowBox[List["124428150", " ", SqrtBox["z"]]], "-", RowBox[List["124428150", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SqrtBox["z"]]], "+", RowBox[List["107692200", " ", "z"]], "+", RowBox[List["107692200", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", "z"]], "+", RowBox[List["49480200", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["49480200", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["11032560", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["11032560", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["332640", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["332640", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["120960", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["120960", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["53760", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["53760", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["30720", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["30720", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["24576", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["24576", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["32768", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["32768", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["131072", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["131072", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["23", "/", "4"]]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List["131072", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["23", "/", "4"]]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], "124428150"]]]]]

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

 2007-05-02