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.acsk.01

 Input Form

 HypergeometricPFQ[{5/4}, {11/2, 21/4}, z] == -((1/(2097152 z^(9/2))) ((5355 (-4 (-161280 + 19665 Sqrt[z] - 65940 z + 3360 z^(3/2) - 12672 z^2 + 256 z^(5/2) - 1024 z^3 + E^(4 Sqrt[z]) (161280 + 19665 Sqrt[z] + 65940 z + 3360 z^(3/2) + 12672 z^2 + 256 z^(5/2) + 1024 z^3)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (342225 + 252720 z + 49920 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (342225 + 252720 z + 49920 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", FractionBox["5", "4"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["11", "2"], ",", FractionBox["21", "4"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["2097152", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]], RowBox[List["(", RowBox[List["5355", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "161280"]], "+", RowBox[List["19665", " ", SqrtBox["z"]]], "-", RowBox[List["65940", " ", "z"]], "+", RowBox[List["3360", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["12672", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["256", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["1024", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["161280", "+", RowBox[List["19665", " ", SqrtBox["z"]]], "+", RowBox[List["65940", " ", "z"]], "+", RowBox[List["3360", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["12672", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["256", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", "3"]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["342225", "+", RowBox[List["252720", " ", "z"]], "+", RowBox[List["49920", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4096", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["342225", "+", RowBox[List["252720", " ", "z"]], "+", RowBox[List["49920", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4096", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]]]

 MathML Form

 1 F 2 ( 5 4 ; 11 2 , 21 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[FractionBox["5", "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[FractionBox["11", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "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 2097152 z 9 / 2 ( 5355 - 2 z ( - 4 ( - 1024 z 3 + 256 z 5 / 2 - 12672 z 2 + 3360 z 3 / 2 - 65940 z + 19665 z + 4 z ( 1024 z 3 + 256 z 5 / 2 + 12672 z 2 + 3360 z 3 / 2 + 65940 z + 19665 z + 161280 ) - 161280 ) + 2 z 2 π z 4 ( 4096 z 3 + 49920 z 2 + 252720 z + 342225 ) erf ( 2 z 4 ) + 2 z 2 π z 4 ( 4096 z 3 + 49920 z 2 + 252720 z + 342225 ) erfi ( 2 z 4 ) ) ) HypergeometricPFQ 5 4 11 2 21 4 z -1 1 2097152 z 9 2 -1 5355 -2 z 1 2 -4 -1024 z 3 256 z 5 2 -1 12672 z 2 3360 z 3 2 -1 65940 z 19665 z 1 2 4 z 1 2 1024 z 3 256 z 5 2 12672 z 2 3360 z 3 2 65940 z 19665 z 1 2 161280 -161280 2 z 1 2 2 1 2 z 1 4 4096 z 3 49920 z 2 252720 z 342225 Erf 2 1 2 z 1 4 2 z 1 2 2 1 2 z 1 4 4096 z 3 49920 z 2 252720 z 342225 Erfi 2 1 2 z 1 4 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", FractionBox["5", "4"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["11", "2"], ",", FractionBox["21", "4"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["5355", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "161280"]], "+", RowBox[List["19665", " ", SqrtBox["z"]]], "-", RowBox[List["65940", " ", "z"]], "+", RowBox[List["3360", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["12672", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["256", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["1024", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["161280", "+", RowBox[List["19665", " ", SqrtBox["z"]]], "+", RowBox[List["65940", " ", "z"]], "+", RowBox[List["3360", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["12672", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["256", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", "3"]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["342225", "+", RowBox[List["252720", " ", "z"]], "+", RowBox[List["49920", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4096", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["342225", "+", RowBox[List["252720", " ", "z"]], "+", RowBox[List["49920", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4096", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], RowBox[List["2097152", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]]]]

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

 2007-05-02