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http://functions.wolfram.com/07.33.03.0673.01
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HypergeometricU[4, 1, z] == (1/72) (-2 (11 + z (8 + z)) -
2 E^z (6 + z (3 + z) (6 + z)) (CoshIntegral[z] - SinhIntegral[z]))
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Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", "1", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "72"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["11", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8", "+", "z"]], ")"]]]]]], ")"]]]], "-", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["3", "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["6", "+", "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> <mn> 1 </mn> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 72 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </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> <mi> z </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6 </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> </mrow> </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'> 1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 72 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> 6 </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> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", "1", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "72"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["11", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["8", "+", "z"]], ")"]]]]]], ")"]]]], "-", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", "z"], " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["3", "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["6", "+", "z"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "z", "]"]]]], ")"]]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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