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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[z] > Inequalities





http://functions.wolfram.com/06.05.29.0006.01









  


  








Input Form





(x/E)^(x - 1) <= Gamma[x] <= (x/2)^(x - 1) /; Element[x, Reals] && x >= 2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["x", "\[ExponentialE]"], ")"]], RowBox[List["x", "-", "1"]]], "\[LessEqual]", RowBox[List["Gamma", "[", "x", "]"]], "\[LessEqual]", SuperscriptBox[RowBox[List["(", FractionBox["x", "2"], ")"]], RowBox[List["x", "-", "1"]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["x", "\[GreaterEqual]", "2", " "]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> x </mi> <mi> &#8519; </mi> </mfrac> <mo> ) </mo> </mrow> <mrow> <mi> x </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8804; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mo> &#8804; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> x </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mi> x </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </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> 2 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> x </mi> <mi> &#8519; </mi> </mfrac> <mo> ) </mo> </mrow> <mrow> <mi> x </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8804; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mo> &#8804; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> x </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mi> x </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </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> 2 </mn> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["x", "\[ExponentialE]"], ")"]], RowBox[List["x", "-", "1"]]], "\[LessEqual]", RowBox[List["Gamma", "[", "x", "]"]], "\[LessEqual]", SuperscriptBox[RowBox[List["(", FractionBox["x", "2"], ")"]], RowBox[List["x", "-", "1"]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", "\[GreaterEqual]", "2"]]]]]]]]


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





2002-12-18