Abs[StirlingS1[n, m]] == Sqrt[StirlingS1[n, m]^2]

Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", RowBox[List["StirlingS1", "[", RowBox[List["n", ",", "m"]], "]"]], "]"]], "\[Equal]", SqrtBox[SuperscriptBox[RowBox[List["StirlingS1", "[", RowBox[List["n", ",", "m"]], "]"]], "2"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <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> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#10869; </mo> <msqrt> <msup> <mrow> <mo> ( </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> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <apply> <ci> StirlingS1 </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <ci> StirlingS1 </ci> <ci> n </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", RowBox[List["StirlingS1", "[", RowBox[List["n_", ",", "m_"]], "]"]], "]"]], "]"]], "\[RuleDelayed]", SqrtBox[SuperscriptBox[RowBox[List["StirlingS1", "[", RowBox[List["n", ",", "m"]], "]"]], "2"]]]]]]

2001-10-29