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.aesm.01

 Input Form

 HypergeometricPFQ[{15/4}, {-(1/2), 23/4}, z] == -((1/(16777216 z^(19/4))) ((285 (4 z^(1/4) (-723647925 - 964863900 Sqrt[z] - 735134400 z - 392071680 z^(3/2) - 156828672 z^2 - 48881664 z^(5/2) - 11976704 z^3 - 2228224 z^(7/2) - 262144 z^4 + E^(4 Sqrt[z]) (723647925 - 964863900 Sqrt[z] + 735134400 z - 392071680 z^(3/2) + 156828672 z^2 - 48881664 z^(5/2) + 11976704 z^3 - 2228224 z^(7/2) + 262144 z^4)) - 2297295 E^(2 Sqrt[z]) Sqrt[2 Pi] (-315 + 16 z) Erf[Sqrt[2] z^(1/4)] + 2297295 E^(2 Sqrt[z]) Sqrt[2 Pi] (-315 + 16 z) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", FractionBox["15", "4"], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["23", "4"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["16777216", " ", SuperscriptBox["z", RowBox[List["19", "/", "4"]]]]]], RowBox[List["(", RowBox[List["285", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "723647925"]], "-", RowBox[List["964863900", " ", SqrtBox["z"]]], "-", RowBox[List["735134400", " ", "z"]], "-", RowBox[List["392071680", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["156828672", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["48881664", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["11976704", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2228224", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["262144", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["723647925", "-", RowBox[List["964863900", " ", SqrtBox["z"]]], "+", RowBox[List["735134400", " ", "z"]], "-", RowBox[List["392071680", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["156828672", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["48881664", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["11976704", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2228224", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["262144", " ", SuperscriptBox["z", "4"]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["2297295", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "315"]], "+", RowBox[List["16", " ", "z"]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List["2297295", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "315"]], "+", RowBox[List["16", " ", "z"]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]]]

 MathML Form

 1 F 2 ( 15 4 ; - 1 2 , 23 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[FractionBox["15", "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["1", "2"]]], 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 16777216 z 19 / 4 ( 285 - 2 z ( 4 z 4 ( - 262144 z 4 - 2228224 z 7 / 2 - 11976704 z 3 - 48881664 z 5 / 2 - 156828672 z 2 - 392071680 z 3 / 2 - 735134400 z - 964863900 z + 4 z ( 262144 z 4 - 2228224 z 7 / 2 + 11976704 z 3 - 48881664 z 5 / 2 + 156828672 z 2 - 392071680 z 3 / 2 + 735134400 z - 964863900 z + 723647925 ) - 723647925 ) - 2297295 2 z 2 π ( 16 z - 315 ) erf ( 2 z 4 ) + 2297295 2 z 2 π ( 16 z - 315 ) erfi ( 2 z 4 ) ) ) HypergeometricPFQ 15 4 -1 1 2 23 4 z -1 1 16777216 z 19 4 -1 285 -2 z 1 2 4 z 1 4 -262144 z 4 -1 2228224 z 7 2 -1 11976704 z 3 -1 48881664 z 5 2 -1 156828672 z 2 -1 392071680 z 3 2 -1 735134400 z -1 964863900 z 1 2 4 z 1 2 262144 z 4 -1 2228224 z 7 2 11976704 z 3 -1 48881664 z 5 2 156828672 z 2 -1 392071680 z 3 2 735134400 z -1 964863900 z 1 2 723647925 -723647925 -1 2297295 2 z 1 2 2 1 2 16 z -315 Erf 2 1 2 z 1 4 2297295 2 z 1 2 2 1 2 16 z -315 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["15", "4"], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["23", "4"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["285", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "723647925"]], "-", RowBox[List["964863900", " ", SqrtBox["z"]]], "-", RowBox[List["735134400", " ", "z"]], "-", RowBox[List["392071680", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["156828672", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["48881664", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["11976704", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2228224", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["262144", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["723647925", "-", RowBox[List["964863900", " ", SqrtBox["z"]]], "+", RowBox[List["735134400", " ", "z"]], "-", RowBox[List["392071680", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["156828672", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["48881664", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["11976704", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2228224", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["262144", " ", SuperscriptBox["z", "4"]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["2297295", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "315"]], "+", RowBox[List["16", " ", "z"]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], "+", RowBox[List["2297295", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SqrtBox["z"]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "315"]], "+", RowBox[List["16", " ", "z"]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], ")"]]]], RowBox[List["16777216", " ", SuperscriptBox["z", RowBox[List["19", "/", "4"]]]]]]]]]]]]

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

 2007-05-02