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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[z] > Limit representations





http://functions.wolfram.com/06.05.09.0002.01









  


  








Input Form





Gamma[z] == Limit[(n! n^z)/Pochhammer[z, n + 1], n -> Infinity]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Gamma", "[", "z", "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["n", "!"]], " ", SuperscriptBox["n", "z"]]], RowBox[List["Pochhammer", "[", RowBox[List["z", ",", RowBox[List["n", "+", "1"]]]], "]"]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> n </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mfrac> <mrow> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> n </mi> <mi> z </mi> </msup> </mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, &quot;z&quot;, &quot;)&quot;]], RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]], Pochhammer] </annotation> </semantics> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Gamma </ci> <ci> z </ci> </apply> <apply> <limit /> <bvar> <ci> n </ci> </bvar> <condition> <apply> <tendsto /> <ci> n </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <factorial /> <ci> n </ci> </apply> <apply> <power /> <ci> n </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> Pochhammer </ci> <ci> z </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["n", "!"]], " ", SuperscriptBox["n", "z"]]], RowBox[List["Pochhammer", "[", RowBox[List["z", ",", RowBox[List["n", "+", "1"]]]], "]"]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]


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





2001-10-29