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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.05.08.0001.01









  


  








Input Form





1/Gamma[z] == z E^(z EulerGamma) Product[(1 + z/k)/E^(z/k), {k, 1, Infinity}]








Standard Form





Cell[BoxData[RowBox[List[FractionBox["1", RowBox[List["Gamma", "[", "z", "]"]]], "\[Equal]", RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", " ", "EulerGamma"]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List["1", "+", FractionBox["z", "k"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", "k"]]]], " "]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> z </mi> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mi> k </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <mi> z </mi> <mi> k </mi> </mfrac> </mrow> </msup> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> Gamma </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> z </ci> <eulergamma /> </apply> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox["1", RowBox[List["Gamma", "[", "z_", "]"]]], "]"]], "\[RuleDelayed]", RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["z", " ", "EulerGamma"]]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List["1", "+", FractionBox["z", "k"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", "k"]]]]]]]]]]]]]]


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





2001-10-29