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variants of this functions
Factorial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Factorial[n] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/06.01.16.0013.01









  


  








Input Form





n! m! == (m + n)!/Binomial[m + n, n]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["n", "!"]], " ", RowBox[List["m", "!"]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["m", "+", "n"]], ")"]], "!"]], RowBox[List["Binomial", "[", RowBox[List[RowBox[List["m", "+", "n"]], ",", "n"]], "]"]]]]]]]








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> <mi> n </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> m </mi> <mo> ! </mo> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mi> m </mi> <mo> + </mo> <mi> n </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;n&quot;]], Identity, Rule[Editable, True]]], List[TagBox[&quot;n&quot;, Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <factorial /> <ci> n </ci> </apply> <apply> <factorial /> <ci> m </ci> </apply> </apply> <apply> <times /> <apply> <factorial /> <apply> <plus /> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <ci> Binomial </ci> <apply> <plus /> <ci> m </ci> <ci> n </ci> </apply> <ci> n </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[RowBox[List["n_", "!"]], " ", RowBox[List["m_", "!"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["m", "+", "n"]], ")"]], "!"]], RowBox[List["Binomial", "[", RowBox[List[RowBox[List["m", "+", "n"]], ",", "n"]], "]"]]]]]]]


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





2001-10-29