|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.25.03.amb0.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HypergeometricPFQ[{4, 11/2}, {-(9/2), 5/2}, z] ==
(1/893025) (893025 - 1746360 z + 2316600 z^2 - 3088800 z^3 + 5569200 z^4 -
26046720 z^5 - 33018624 z^6 - 12928320 z^7 - 2278080 z^8 - 197856 z^9 -
8192 z^10 - 128 z^11) - (1/893025) (16 E^z Sqrt[Pi] z^(11/2)
(2386800 + 2409750 z + 873630 z^2 + 148317 z^3 + 12618 z^4 + 516 z^5 +
8 z^6) Erf[Sqrt[z]])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["4", ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", FractionBox["5", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "893025"], RowBox[List["(", RowBox[List["893025", "-", RowBox[List["1746360", " ", "z"]], "+", RowBox[List["2316600", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3088800", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5569200", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["26046720", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["33018624", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["12928320", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["2278080", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["197856", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["8192", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["128", " ", SuperscriptBox["z", "11"]]]]], ")"]]]], "-", RowBox[List[FractionBox["1", "893025"], RowBox[List["(", RowBox[List["16", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2386800", "+", RowBox[List["2409750", " ", "z"]], "+", RowBox[List["873630", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["148317", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["12618", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["516", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], ")"]]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> , </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "2"], 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[FractionBox["5", "2"], 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] </annotation> </semantics> <mo>  </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 893025 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 128 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8192 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 197856 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2278080 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12928320 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 33018624 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 26046720 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5569200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3088800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2316600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1746360 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 893025 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 893025 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 516 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12618 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 148317 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 873630 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2409750 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2386800 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 4 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 893025 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -128 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8192 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 197856 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2278080 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12928320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 33018624 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 26046720 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5569200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3088800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2316600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1746360 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 893025 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 893025 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 516 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12618 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 148317 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 873630 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2409750 </cn> <ci> z </ci> </apply> <cn type='integer'> 2386800 </cn> </apply> <apply> <ci> Erf </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["4", ",", FractionBox["11", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", FractionBox["5", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["893025", "-", RowBox[List["1746360", " ", "z"]], "+", RowBox[List["2316600", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3088800", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5569200", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["26046720", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["33018624", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["12928320", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["2278080", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["197856", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["8192", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["128", " ", SuperscriptBox["z", "11"]]]]], "893025"], "-", FractionBox[RowBox[List["16", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2386800", "+", RowBox[List["2409750", " ", "z"]], "+", RowBox[List["873630", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["148317", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["12618", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["516", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], "893025"]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | |
|
|
|