HypergeometricU[5, -3, z] == (1/967680) (144 - z (240 + z (-360 + z (840 + z (1066 + z (306 + z (31 + z)))))) - E^z z^4 (1680 + z (1344 + z (336 + z (32 + z)))) (CoshIntegral[z] - 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[&quot;U&quot;, HypergeometricU] </annotation> </semantics> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 967680 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <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> 32 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 336 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1344 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1680 </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> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <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> 31 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 306 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1066 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 840 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 360 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 240 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 144 </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'> -3 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 967680 </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'> 32 </cn> </apply> </apply> <cn type='integer'> 336 </cn> </apply> </apply> <cn type='integer'> 1344 </cn> </apply> </apply> <cn type='integer'> 1680 </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 /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 31 </cn> </apply> </apply> <cn type='integer'> 306 </cn> </apply> </apply> <cn type='integer'> 1066 </cn> </apply> </apply> <cn type='integer'> 840 </cn> </apply> </apply> <cn type='integer'> -360 </cn> </apply> </apply> <cn type='integer'> 240 </cn> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 144 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02