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http://functions.wolfram.com/07.33.03.0840.01
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HypergeometricU[6, -(7/2), -z] ==
-((1/9820936125)
((4 (Sqrt[Pi] (-z)^(9/2) (692835 -
2 z (314925 + 4 z (-24225 + 2 z (1615 + z (-95 + 2 z))))) +
2 E^z (-12600 + z (-21600 + z (-30240 + z (-53760 + z (-241920 +
z (274845 + 4 z (-22745 + 2 z (1569 + 2 (-47 + z) z)))))))) +
Sqrt[Pi] z^(9/2) (692835 - 2 z (314925 +
4 z (-24225 + 2 z (1615 + z (-95 + 2 z))))) Erfi[Sqrt[z]]))/E^z))
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", "9820936125"], RowBox[List["(", RowBox[List["4", " ", 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["692835", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["314925", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24225"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1615", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "95"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "12600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "30240"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "53760"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "241920"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["274845", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "22745"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1569", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "47"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["692835", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["314925", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24225"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1615", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "95"]], "+", 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> 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> 9820936125 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 4 </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> 692835 </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> 95 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1615 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 24225 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 314925 </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> <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> <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> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 47 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1569 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 22745 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 274845 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 241920 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 53760 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 30240 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 21600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 12600 </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> 692835 </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> 95 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1615 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 24225 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 314925 </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'> 6 </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 /> 9820936125 </cn> <apply> <times /> <cn type='integer'> 4 </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'> 692835 </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'> -95 </cn> </apply> </apply> <cn type='integer'> 1615 </cn> </apply> </apply> <cn type='integer'> -24225 </cn> </apply> </apply> <cn type='integer'> 314925 </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 /> <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 /> <cn type='integer'> 4 </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> <apply> <plus /> <ci> z </ci> <cn type='integer'> -47 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 1569 </cn> </apply> </apply> <cn type='integer'> -22745 </cn> </apply> </apply> <cn type='integer'> 274845 </cn> </apply> </apply> <cn type='integer'> -241920 </cn> </apply> </apply> <cn type='integer'> -53760 </cn> </apply> </apply> <cn type='integer'> -30240 </cn> </apply> </apply> <cn type='integer'> -21600 </cn> </apply> </apply> <cn type='integer'> -12600 </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'> 692835 </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'> -95 </cn> </apply> </apply> <cn type='integer'> 1615 </cn> </apply> </apply> <cn type='integer'> -24225 </cn> </apply> </apply> <cn type='integer'> 314925 </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>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["6", ",", RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["4", " ", 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["692835", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["314925", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24225"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1615", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "95"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "12600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21600"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "30240"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "53760"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "241920"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["274845", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "22745"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1569", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "47"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List["692835", "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["314925", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24225"]], "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1615", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "95"]], "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", SqrtBox["z"], "]"]]]]]], ")"]]]], "9820936125"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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