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StirlingS1




Mathematica Notation

Traditional Notation









Integer Functions > StirlingS1[n,m] > General characteristics > Domain and analyticity





http://functions.wolfram.com/04.14.04.0001.01









  


  








Input Form





DomainAndRange[Function[{n, m}, StirlingS1[n, m]]] == ProductSet[Integers, Integers] \[LongRightArrow] Integers








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["n", ",", " ", "m"]], "}"]], ",", " ", RowBox[List["StirlingS1", "[", RowBox[List["n", ",", "m"]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Integers", ",", "Integers"]], "]"]], "\[LongRightArrow]", "Integers"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> &#8902; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <msubsup> <semantics> <mi> S </mi> <annotation encoding='Mathematica'> TagBox[&quot;S&quot;, StirlingS1] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </msubsup> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#8469; </mi> <mo> &#8855; </mo> <mi> &#8469; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <ci> n </ci> <ci> m </ci> </apply> <apply> <ci> StirlingS1 </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <ci> &#8469; </ci> <ci> &#8469; </ci> </apply> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["n_", ",", "m_"]], "}"]], ",", RowBox[List["StirlingS1", "[", RowBox[List["n_", ",", "m_"]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Integers", ",", "Integers"]], "]"]], "\[LongRightArrow]", "Integers"]]]]]]


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





2001-10-29