|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.25.03.ant9.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HypergeometricPFQ[{11/2, 6}, {-(7/2), 3/2}, z] ==
(1/1488375) (1488375 - 9355500 z + 34054020 z^2 - 129729600 z^3 +
1102701600 z^4 + 3428399520 z^5 + 3106071360 z^6 + 1306894176 z^7 +
298011960 z^8 + 39355050 z^9 + 3068904 z^10 + 138192 z^11 + 3296 z^12 +
32 z^13) + (1/1488375) (E^z Sqrt[Pi] z^(9/2) (2095133040 + 4571199360 z +
3648168720 z^2 + 1439488260 z^3 + 316313235 z^4 + 40824378 z^5 +
3136392 z^6 + 139824 z^7 + 3312 z^8 + 32 z^9) Erf[Sqrt[z]])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["11", "2"], ",", "6"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "1488375"], RowBox[List["(", RowBox[List["1488375", "-", RowBox[List["9355500", " ", "z"]], "+", RowBox[List["34054020", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["129729600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1102701600", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3428399520", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["3106071360", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1306894176", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["298011960", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["39355050", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["3068904", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["138192", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["3296", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "13"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "1488375"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2095133040", "+", RowBox[List["4571199360", " ", "z"]], "+", RowBox[List["3648168720", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1439488260", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["316313235", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["40824378", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["3136392", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["139824", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["3312", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", 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> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 3 </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[FractionBox["11", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", 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["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "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> 1488375 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 32 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3312 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 139824 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3136392 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40824378 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 316313235 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1439488260 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3648168720 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4571199360 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2095133040 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 1488375 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 32 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3296 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 138192 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3068904 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 39355050 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 298011960 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1306894176 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3106071360 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3428399520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1102701600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 129729600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 34054020 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 9355500 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1488375 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 11 <sep /> 2 </cn> <cn type='integer'> 6 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 1488375 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3312 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 139824 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3136392 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40824378 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 316313235 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1439488260 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3648168720 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4571199360 </cn> <ci> z </ci> </apply> <cn type='integer'> 2095133040 </cn> </apply> <apply> <ci> Erf </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 1488375 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 138192 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3068904 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 39355050 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 298011960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1306894176 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3106071360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3428399520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1102701600 </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'> 129729600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 34054020 </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'> 9355500 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1488375 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["11", "2"], ",", "6"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["1488375", "-", RowBox[List["9355500", " ", "z"]], "+", RowBox[List["34054020", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["129729600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1102701600", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3428399520", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["3106071360", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1306894176", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["298011960", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["39355050", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["3068904", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["138192", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["3296", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "13"]]]]], "1488375"], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2095133040", "+", RowBox[List["4571199360", " ", "z"]], "+", RowBox[List["3648168720", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1439488260", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["316313235", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["40824378", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["3136392", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["139824", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["3312", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "9"]]]]], ")"]], " ", RowBox[List["Erf", "[", SqrtBox["z"], "]"]]]], "1488375"]]]]]]] |
|
|
|
|
|
|
|
|
|
|
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] | |
|
|
|