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Subfactorial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Subfactorial[n] > Differentiation > Low-order differentiation





http://functions.wolfram.com/06.42.20.0003.01









  


  








Input Form





D[Subfactorial[z], {z, 2}] == (-Pi^2) Subfactorial[z] + (1/E) (2 I Pi MeijerG[{{}, {1, 1}}, {{0, 0, 1 + z}, {}}, -1] + 2 MeijerG[{{}, {1, 1, 1}}, {{0, 0, 0, 1 + z}, {}}, -1])








Standard Form





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MathML Form







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</mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> Subfactorial </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> Subfactorial </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <pi /> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </list> <list /> </list> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </list> <list /> </list> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subfactorial </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02