|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.33.03.0655.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HypergeometricU[4, -(7/2), -z] ==
-((1/6081075) ((16 (Sqrt[Pi] (-z)^(9/2) (2145 - 2 z (585 - 90 z + 4 z^2)) +
E^z (-315 + 2 z (-180 + z (-180 + z (-240 + z (-840 +
z (543 + 4 (-22 + z) z)))))) + Sqrt[Pi] z^(9/2)
(2145 - 2 z (585 - 90 z + 4 z^2)) Erfi[Sqrt[z]]))/E^z))
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", "6081075"], RowBox[List["(", RowBox[List["16", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2145", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["585", "-", RowBox[List["90", " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "315"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "180"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "180"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "240"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "840"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["543", "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "22"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2145", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["585", "-", RowBox[List["90", " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]]]], ")"]]]], ")"]]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> U </mi> <annotation encoding='Mathematica'> TagBox["U", HypergeometricU] </annotation> </semantics> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6081075 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2145 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 90 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 585 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 22 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 543 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 840 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 240 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 180 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 180 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 315 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2145 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 90 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 585 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 6081075 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 2145 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </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'> 90 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 585 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -22 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 543 </cn> </apply> </apply> <cn type='integer'> -840 </cn> </apply> </apply> <cn type='integer'> -240 </cn> </apply> </apply> <cn type='integer'> -180 </cn> </apply> </apply> <cn type='integer'> -180 </cn> </apply> </apply> <cn type='integer'> -315 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 2145 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </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'> 90 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 585 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["16", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2145", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["585", "-", RowBox[List["90", " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "315"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "180"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "180"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "240"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "840"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["543", "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "22"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["2145", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["585", "-", RowBox[List["90", " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]]]], ")"]]]], "6081075"]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|