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http://functions.wolfram.com/07.33.03.0656.01
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HypergeometricU[4, -3, z] ==
(1/30240) (36 - z (48 + z (-60 + z (120 + z (107 + z (20 + z))))) -
E^z z^4 (210 + z (126 + z (21 + z))) (CoshIntegral[z] - SinhIntegral[z]))
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", RowBox[List["-", "3"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "30240"], RowBox[List["(", RowBox[List["36", "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List["48", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "60"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["107", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["20", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["210", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["126", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21", "+", "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> 4 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 30240 </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> <mi> z </mi> <mo> + </mo> <mn> 21 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 126 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 210 </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> 4 </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> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 20 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 107 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 120 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 60 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 48 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 36 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 4 </cn> <cn type='integer'> -3 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 30240 </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 /> <ci> z </ci> <cn type='integer'> 21 </cn> </apply> </apply> <cn type='integer'> 126 </cn> </apply> </apply> <cn type='integer'> 210 </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'> 4 </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 /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 20 </cn> </apply> </apply> <cn type='integer'> 107 </cn> </apply> </apply> <cn type='integer'> 120 </cn> </apply> </apply> <cn type='integer'> -60 </cn> </apply> </apply> <cn type='integer'> 48 </cn> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 36 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", RowBox[List["-", "3"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["36", "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List["48", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "60"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["107", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["20", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["210", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["126", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "z", "]"]]]], ")"]]]]]], "30240"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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