HypergeometricU[4, 2, z] == (1/(12 z)) (2 + z (5 + z) + E^z z (6 + z (6 + z)) (CoshIntegral[z] - SinhIntegral[z]))

Cell[BoxData[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["12", " ", "z"]]], RowBox[List["(", RowBox[List["2", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["5", "+", "z"]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", "z", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["6", "+", "z"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "z", "]"]]]], ")"]]]]]], ")"]]]]]]]]

<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[&quot;U&quot;, HypergeometricU] </annotation> </semantics> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </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> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Chi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Shi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 4 </cn> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <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> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List["4", ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["5", "+", "z"]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], " ", "z", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["6", "+", "z"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["CoshIntegral", "[", "z", "]"]], "-", RowBox[List["SinhIntegral", "[", "z", "]"]]]], ")"]]]]]], RowBox[List["12", " ", "z"]]]]]]]

2007-05-02