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/07.22.03.7592.01

 Input Form

 HypergeometricPFQ[{5}, {1/4, 23/4}, z] == (1/(134217728 z^(19/4))) ((21945 (-240 E^(2 Sqrt[z]) z^(3/4) (72765 + 21868 z + 3024 z^2 + 256 z^3) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-3274425 + 6548850 Sqrt[z] - 6597360 z + 4462920 z^(3/2) - 2283120 z^2 + 944160 z^(5/2) - 330240 z^3 + 101376 z^(7/2) - 28672 z^4 + 8192 z^(9/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (3274425 + 6548850 Sqrt[z] + 6597360 z + 4462920 z^(3/2) + 2283120 z^2 + 944160 z^(5/2) + 330240 z^3 + 101376 z^(7/2) + 28672 z^4 + 8192 z^(9/2)) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "5", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["23", "4"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["134217728", " ", SuperscriptBox["z", RowBox[List["19", "/", "4"]]]]]], RowBox[List["(", RowBox[List["21945", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "240"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["72765", "+", RowBox[List["21868", " ", "z"]], "+", RowBox[List["3024", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["256", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3274425"]], "+", RowBox[List["6548850", " ", SqrtBox["z"]]], "-", RowBox[List["6597360", " ", "z"]], "+", RowBox[List["4462920", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["2283120", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["944160", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["330240", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["101376", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["28672", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["8192", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List["3274425", "+", RowBox[List["6548850", " ", SqrtBox["z"]]], "+", RowBox[List["6597360", " ", "z"]], "+", RowBox[List["4462920", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["2283120", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["944160", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["330240", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["101376", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["28672", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["8192", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 1 F 2 ( 5 ; 1 4 , 23 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox["5", 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["1", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["23", "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 134217728 z 19 / 4 ( 21945 - 2 z ( - 240 2 z z 3 / 4 ( 256 z 3 + 3024 z 2 + 21868 z + 72765 ) + 4 z 2 π ( 8192 z 9 / 2 - 28672 z 4 + 101376 z 7 / 2 - 330240 z 3 + 944160 z 5 / 2 - 2283120 z 2 + 4462920 z 3 / 2 - 6597360 z + 6548850 z - 3274425 ) erf ( 2 z 4 ) + 2 π ( 8192 z 9 / 2 + 28672 z 4 + 101376 z 7 / 2 + 330240 z 3 + 944160 z 5 / 2 + 2283120 z 2 + 4462920 z 3 / 2 + 6597360 z + 6548850 z + 3274425 ) erfi ( 2 z 4 ) ) ) HypergeometricPFQ 5 1 4 23 4 z 1 134217728 z 19 4 -1 21945 -2 z 1 2 -240 2 z 1 2 z 3 4 256 z 3 3024 z 2 21868 z 72765 4 z 1 2 2 1 2 8192 z 9 2 -1 28672 z 4 101376 z 7 2 -1 330240 z 3 944160 z 5 2 -1 2283120 z 2 4462920 z 3 2 -1 6597360 z 6548850 z 1 2 -3274425 Erf 2 1 2 z 1 4 2 1 2 8192 z 9 2 28672 z 4 101376 z 7 2 330240 z 3 944160 z 5 2 2283120 z 2 4462920 z 3 2 6597360 z 6548850 z 1 2 3274425 Erfi 2 1 2 z 1 4 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "5", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["23", "4"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["21945", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "240"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["72765", "+", RowBox[List["21868", " ", "z"]], "+", RowBox[List["3024", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["256", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3274425"]], "+", RowBox[List["6548850", " ", SqrtBox["z"]]], "-", RowBox[List["6597360", " ", "z"]], "+", RowBox[List["4462920", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["2283120", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["944160", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["330240", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["101376", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["28672", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["8192", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List["3274425", "+", RowBox[List["6548850", " ", SqrtBox["z"]]], "+", RowBox[List["6597360", " ", "z"]], "+", RowBox[List["4462920", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["2283120", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["944160", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["330240", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["101376", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["28672", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["8192", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], RowBox[List["134217728", " ", SuperscriptBox["z", RowBox[List["19", "/", "4"]]]]]]]]]]

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

 2007-05-02