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variants of this functions
Factorial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Factorial[n] > Inequalities





http://functions.wolfram.com/06.01.29.0002.01









  


  








Input Form





n! <= (n + 1)^(n + 1)/E^n /; Element[n, Integers] && n >= 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["n", "!"]], "\[LessEqual]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["n", "+", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "n"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]








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> &#8804; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <leq /> <apply> <factorial /> <ci> n </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["n", "!"]], "\[LessEqual]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["n", "+", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "n"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]


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





2001-10-29