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http://functions.wolfram.com/07.33.03.0837.01
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HypergeometricU[6, -(9/2), -z] ==
-((1/206239658625)
((8 (Sqrt[Pi] Sqrt[-z] z^5 (1322685 -
2 z (508725 + 4 z (-33915 + 2 z (1995 + z (-105 + 2 z))))) +
2 E^z (-56700 + z (-75600 + z (-75600 + z (-80640 + z (-120960 +
z (-483840 + z (451395 + 8 z (-16035 + 2 z (972 + (-52 + z)
z))))))))) + Sqrt[Pi] z^(11/2)
(1322685 - 2 z (508725 + 4 z (-33915 + 2 z (1995 + z (-105 + 2 z)))))
Erfi[Sqrt[z]]))/E^z))
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", "206239658625"], RowBox[List["(", RowBox[List["8", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox[RowBox[List["-", "z"]]], " ", SuperscriptBox["z", "5"], " ", RowBox[List["(", RowBox[List["1322685", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["508725", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33915"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1995", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "105"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "56700"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "75600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "75600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "80640"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "120960"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "483840"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["451395", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16035"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["972", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "52"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1322685", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["508725", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33915"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1995", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "105"]], "+", RowBox[List["2", " ", "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> 6 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 9 </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> 206239658625 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 8 </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> 1322685 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 105 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1995 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 33915 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 508725 </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> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1322685 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 105 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1995 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 33915 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 508725 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </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> <mn> 8 </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> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 52 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 972 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 16035 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 451395 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 483840 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 120960 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 80640 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 75600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 75600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 56700 </mn> </mrow> <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'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <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 /> 206239658625 </cn> <apply> <times /> <cn type='integer'> 8 </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'> 1322685 </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> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -105 </cn> </apply> </apply> <cn type='integer'> 1995 </cn> </apply> </apply> <cn type='integer'> -33915 </cn> </apply> </apply> <cn type='integer'> 508725 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1322685 </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> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -105 </cn> </apply> </apply> <cn type='integer'> 1995 </cn> </apply> </apply> <cn type='integer'> -33915 </cn> </apply> </apply> <cn type='integer'> 508725 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </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 /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -52 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 972 </cn> </apply> </apply> <cn type='integer'> -16035 </cn> </apply> </apply> <cn type='integer'> 451395 </cn> </apply> </apply> <cn type='integer'> -483840 </cn> </apply> </apply> <cn type='integer'> -120960 </cn> </apply> </apply> <cn type='integer'> -80640 </cn> </apply> </apply> <cn type='integer'> -75600 </cn> </apply> </apply> <cn type='integer'> -75600 </cn> </apply> </apply> <cn type='integer'> -56700 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["9", "2"]]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["8", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox[RowBox[List["-", "z"]]], " ", SuperscriptBox["z", "5"], " ", RowBox[List["(", RowBox[List["1322685", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["508725", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33915"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1995", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "105"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "56700"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "75600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "75600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "80640"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "120960"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "483840"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["451395", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16035"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["972", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "52"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1322685", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["508725", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33915"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1995", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "105"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]]]], ")"]]]], "206239658625"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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