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.a8o4.01

 Input Form

 HypergeometricPFQ[{-(13/4)}, {5/2, 3/4}, z] == (1/(4213440 z^(3/2))) ((-4 (-5265 - 10530 Sqrt[z] + 56160 z - 400320 z^(3/2) - 89865 z^2 + 391668 z^(5/2) + 11616 z^3 - 47232 z^(7/2) - 256 z^4 + 1024 z^(9/2) + E^(4 Sqrt[z]) (5265 - 10530 Sqrt[z] - 56160 z - 400320 z^(3/2) + 89865 z^2 + 391668 z^(5/2) - 11616 z^3 - 47232 z^(7/2) + 256 z^4 + 1024 z^(9/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (-1833975 + 1600560 z - 189696 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (-1833975 + 1600560 z - 189696 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["{", RowBox[List["-", FractionBox["13", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["4213440", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5265"]], "-", RowBox[List["10530", " ", SqrtBox["z"]]], "+", RowBox[List["56160", " ", "z"]], "-", RowBox[List["400320", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["89865", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["391668", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["11616", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["47232", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["256", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["5265", "-", RowBox[List["10530", " ", SqrtBox["z"]]], "-", RowBox[List["56160", " ", "z"]], "-", RowBox[List["400320", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["89865", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["391668", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["11616", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["47232", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["256", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1833975"]], "+", RowBox[List["1600560", " ", "z"]], "-", RowBox[List["189696", " ", 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["7", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1833975"]], "+", RowBox[List["1600560", " ", "z"]], "-", RowBox[List["189696", " ", 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 ( - 13 4 ; 5 2 , 3 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["13", "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["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "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 4213440 z 3 / 2 ( - 2 z ( - 2 z 2 π ( 4096 z 3 - 189696 z 2 + 1600560 z - 1833975 ) erf ( 2 z 4 ) z 7 / 4 + 2 z 2 π ( 4096 z 3 - 189696 z 2 + 1600560 z - 1833975 ) erfi ( 2 z 4 ) z 7 / 4 - 4 ( 1024 z 9 / 2 - 256 z 4 - 47232 z 7 / 2 + 11616 z 3 + 391668 z 5 / 2 - 89865 z 2 - 400320 z 3 / 2 + 56160 z - 10530 z + 4 z ( 1024 z 9 / 2 + 256 z 4 - 47232 z 7 / 2 - 11616 z 3 + 391668 z 5 / 2 + 89865 z 2 - 400320 z 3 / 2 - 56160 z - 10530 z + 5265 ) - 5265 ) ) ) HypergeometricPFQ -1 13 4 5 2 3 4 z 1 4213440 z 3 2 -1 -2 z 1 2 -1 2 z 1 2 2 1 2 4096 z 3 -1 189696 z 2 1600560 z -1833975 Erf 2 1 2 z 1 4 z 7 4 2 z 1 2 2 1 2 4096 z 3 -1 189696 z 2 1600560 z -1833975 Erfi 2 1 2 z 1 4 z 7 4 -1 4 1024 z 9 2 -1 256 z 4 -1 47232 z 7 2 11616 z 3 391668 z 5 2 -1 89865 z 2 -1 400320 z 3 2 56160 z -1 10530 z 1 2 4 z 1 2 1024 z 9 2 256 z 4 -1 47232 z 7 2 -1 11616 z 3 391668 z 5 2 89865 z 2 -1 400320 z 3 2 -1 56160 z -1 10530 z 1 2 5265 -5265 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["-", FractionBox["13", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5265"]], "-", RowBox[List["10530", " ", SqrtBox["z"]]], "+", RowBox[List["56160", " ", "z"]], "-", RowBox[List["400320", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["89865", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["391668", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["11616", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["47232", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["256", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["5265", "-", RowBox[List["10530", " ", SqrtBox["z"]]], "-", RowBox[List["56160", " ", "z"]], "-", RowBox[List["400320", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["89865", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["391668", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["11616", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["47232", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["256", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1024", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1833975"]], "+", RowBox[List["1600560", " ", "z"]], "-", RowBox[List["189696", " ", 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["7", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1833975"]], "+", RowBox[List["1600560", " ", "z"]], "-", RowBox[List["189696", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4096", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], RowBox[List["4213440", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2007-05-02