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variants of this functions
EulerE




Mathematica Notation

Traditional Notation









Integer Functions > EulerE[n] > Series representations > Residue representations





http://functions.wolfram.com/04.12.06.0004.01









  


  








Input Form





EulerE[n] == n! Residue[Sech[z] z^(-n - 1), {z, 0}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["EulerE", "[", "n", "]"]], "\[Equal]", RowBox[List[RowBox[List["n", "!"]], " ", RowBox[List["Residue", "[", RowBox[List[RowBox[List[RowBox[List["Sech", "[", "z", "]"]], SuperscriptBox["z", RowBox[List[RowBox[List["-", "n"]], "-", "1"]]]]], ",", RowBox[List["{", RowBox[List["z", ",", "0"]], "}"]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox[&quot;E&quot;, EulerE] </annotation> </semantics> <mi> n </mi> </msub> <mo> &#10869; </mo> <mrow> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> res </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <mi> sech </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> EulerE </ci> <ci> n </ci> </apply> <apply> <times /> <apply> <factorial /> <ci> n </ci> </apply> <apply> <apply> <ci> Subscript </ci> <ci> res </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <sech /> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EulerE", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["n", "!"]], " ", RowBox[List["Residue", "[", RowBox[List[RowBox[List[RowBox[List["Sech", "[", "z", "]"]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "n"]], "-", "1"]]]]], ",", RowBox[List["{", RowBox[List["z", ",", "0"]], "}"]]]], "]"]]]]]]]]


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





2001-10-29