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http://functions.wolfram.com/07.33.03.0760.01
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HypergeometricU[5, -1, z] ==
(1/17280) (24 - z (120 + z (342 + z (158 + z (23 + z)))) -
E^z z^2 (360 + z (480 + z (180 + z (24 + z))))
(CoshIntegral[z] - SinhIntegral[z]))
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["5", ",", RowBox[List["-", "1"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "17280"], RowBox[List["(", RowBox[List["24", "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["342", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["158", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["23", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["360", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["480", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["180", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["24", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "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> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 17280 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> </mrow> <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> <mi> z </mi> <mo> + </mo> <mn> 24 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 180 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 480 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 360 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Chi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Shi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <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> <mi> z </mi> <mo> + </mo> <mn> 23 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 158 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 342 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 120 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 24 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 5 </cn> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 17280 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 24 </cn> </apply> </apply> <cn type='integer'> 180 </cn> </apply> </apply> <cn type='integer'> 480 </cn> </apply> </apply> <cn type='integer'> 360 </cn> </apply> <apply> <plus /> <apply> <ci> CoshIntegral </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> SinhIntegral </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 23 </cn> </apply> </apply> <cn type='integer'> 158 </cn> </apply> </apply> <cn type='integer'> 342 </cn> </apply> </apply> <cn type='integer'> 120 </cn> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 24 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["5", ",", RowBox[List["-", "1"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["24", "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["342", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["158", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["23", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["360", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["480", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["180", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["24", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "z", "]"]]]], ")"]]]]]], "17280"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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