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StirlingS2




Mathematica Notation

Traditional Notation









Integer Functions > StirlingS2[n,m] > Operations > Limit operation





http://functions.wolfram.com/04.15.25.0001.01









  


  








Input Form





Limit[StirlingS2[n, m]/m^n, n -> Infinity] == 1/m!








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["StirlingS2", "[", RowBox[List["n", ",", "m"]], "]"]], SuperscriptBox["m", "n"]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", FractionBox["1", RowBox[List["m", "!"]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munder> <mi> lim </mi> <mrow> <mi> n </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mfrac> <msubsup> <semantics> <mi> &#119982; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[ScriptCapitalS]&quot;, StirlingS2] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </msubsup> <msup> <mi> m </mi> <mi> n </mi> </msup> </mfrac> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> m </mi> <mo> ! </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> n </ci> </bvar> <condition> <apply> <tendsto /> <ci> n </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <ci> StirlingS2 </ci> <ci> n </ci> <ci> m </ci> </apply> <apply> <power /> <apply> <power /> <ci> m </ci> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <factorial /> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["StirlingS2", "[", RowBox[List["n_", ",", "m_"]], "]"]], SuperscriptBox["m_", "n_"]], ",", RowBox[List["n_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List["m", "!"]]]]]]]


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





2001-10-29