n! (-n)! == n Pi Csc[n Pi]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <factorial /> <ci> n </ci> </apply> <apply> <factorial /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <times /> <ci> n </ci> <pi /> <apply> <csc /> <apply> <times /> <ci> n </ci> <pi /> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["n_", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["-", "n_"]], ")"]], "!"]]]], "]"]], "\[RuleDelayed]", RowBox[List["n", " ", "\[Pi]", " ", RowBox[List["Csc", "[", RowBox[List["n", " ", "\[Pi]"]], "]"]]]]]]]]

2001-10-29