Subfactorial[-5] == 5/12 - (I Pi + ExpIntegralEi[1])/(24 E)

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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> <mi> Subfactorial </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 12 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> + </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <mi> &#8519; </mi> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subfactorial </ci> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <cn type='rational'> 5 <sep /> 12 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <pi /> </apply> <apply> <ci> ExpIntegralEi </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 24 </cn> <exponentiale /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02