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http://functions.wolfram.com/07.33.03.0747.01
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HypergeometricU[5, -(11/2), -z] == (1/41247931725)
((16 (Sqrt[Pi] (-z)^(13/2) (-101745 +
8 z (6783 + z (-1197 - 2 (-42 + z) z))) +
2 E^z (31185 + z (28350 + z (18900 +
z (12600 + z (10080 + z (12096 + z (40320 + z (-24975 +
2 z (2313 + 2 z (-83 + 2 z)))))))))) +
Sqrt[Pi] z^(13/2) (-101745 + 8 z (6783 + z (-1197 - 2 (-42 + z) z)))
Erfi[Sqrt[z]]))/E^z)
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["5", ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "41247931725"], 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["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "101745"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["6783", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1197"]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "42"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List["31185", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["28350", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["18900", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["12600", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["10080", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["12096", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["40320", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24975"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2313", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "83"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "101745"]], "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["6783", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1197"]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "42"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]]]], ")"]]]], ")"]]]]]]]]
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<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> 5 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 41247931725 </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> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 42 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1197 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6783 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 101745 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <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> <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> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 83 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2313 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 24975 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 40320 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 12096 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 10080 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 12600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 18900 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 28350 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 31185 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 42 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1197 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6783 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 101745 </mn> </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> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 41247931725 </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 /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -42 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1197 </cn> </apply> </apply> <cn type='integer'> 6783 </cn> </apply> </apply> <cn type='integer'> -101745 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -83 </cn> </apply> </apply> <cn type='integer'> 2313 </cn> </apply> </apply> <cn type='integer'> -24975 </cn> </apply> </apply> <cn type='integer'> 40320 </cn> </apply> </apply> <cn type='integer'> 12096 </cn> </apply> </apply> <cn type='integer'> 10080 </cn> </apply> </apply> <cn type='integer'> 12600 </cn> </apply> </apply> <cn type='integer'> 18900 </cn> </apply> </apply> <cn type='integer'> 28350 </cn> </apply> </apply> <cn type='integer'> 31185 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -42 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1197 </cn> </apply> </apply> <cn type='integer'> 6783 </cn> </apply> </apply> <cn type='integer'> -101745 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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