Gamma[x] <= x^x E^(1 - x) /; Element[x, Reals] && x >= 1

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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> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mrow> <msup> <mi> x </mi> <mi> x </mi> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> x </mi> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> &#8712; </mo> <mi> &#8477; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> x </mi> <mo> &#8805; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <leq /> <apply> <ci> Gamma </ci> <ci> x </ci> </apply> <apply> <times /> <apply> <power /> <ci> x </ci> <ci> x </ci> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> x </ci> <ci> &#8477; </ci> </apply> <apply> <geq /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Gamma", "[", "x", "]"]], "\[LessEqual]", RowBox[List[SuperscriptBox["x", "x"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["1", "-", "x"]]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", "\[GreaterEqual]", "1"]]]]]]]]

2001-10-29