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variants of this functions
Factorial




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.01.29.0001.01









  


  








Input Form





k!^n n^(k n) >= n!^k k^(k n) /; Element[n, Integers] && n > 0 && Element[k, Integers] && k > 0 && n >= k








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["k", "!"]], "n"], " ", SuperscriptBox["n", RowBox[List["k", " ", "n"]]]]], "\[GreaterEqual]", RowBox[List[SuperscriptBox[RowBox[List["n", "!"]], "k"], " ", SuperscriptBox["k", RowBox[List["k", " ", "n"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", ">", "0"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "k"]]]]]]]]








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> <msup> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <msup> <mi> n </mi> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msup> </mrow> <mo> &#8805; </mo> <mrow> <msup> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <msup> <mi> k </mi> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8805; </mo> <mi> k </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <geq /> <apply> <times /> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <ci> n </ci> </apply> <apply> <power /> <ci> n </ci> <apply> <times /> <ci> k </ci> <ci> n </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <factorial /> <ci> n </ci> </apply> <ci> k </ci> </apply> <apply> <power /> <ci> k </ci> <apply> <times /> <ci> k </ci> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> <apply> <in /> <ci> k </ci> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> <apply> <geq /> <ci> n </ci> <ci> k </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["k", "!"]], ")"]], "n"], " ", SuperscriptBox["n", RowBox[List["k", " ", "n"]]]]], "\[GreaterEqual]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["n", "!"]], ")"]], "k"], " ", SuperscriptBox["k", RowBox[List["k", " ", "n"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]], "&&", RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]], "&&", RowBox[List["n", "\[GreaterEqual]", "k"]]]]]]]]


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





2001-10-29