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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[a,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > Special cases





http://functions.wolfram.com/06.06.06.0036.01









  


  








Input Form





Gamma[-1, z] \[Proportional] Log[z] + 1/z - 1 + EulerGamma - z/2 + z^2/12 - z^3/72 + O[z^4]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "1"]], ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "+", FractionBox["1", "z"], "-", "1", "+", "EulerGamma", "-", FractionBox["z", "2"], "+", FractionBox[SuperscriptBox["z", "2"], "12"], "-", FractionBox[SuperscriptBox["z", "3"], "72"], "+", RowBox[List["O", "[", SuperscriptBox["z", "4"], "]"]]]]]]]]








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> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> + </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> <mo> - </mo> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 12 </mn> </mfrac> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mn> 72 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> Gamma </ci> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <plus /> <apply> <ln /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <eulergamma /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 12 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 72 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "1"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "+", FractionBox["1", "z"], "-", "1", "+", "EulerGamma", "-", FractionBox["z", "2"], "+", FractionBox[SuperscriptBox["z", "2"], "12"], "-", FractionBox[SuperscriptBox["z", "3"], "72"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "4"]]]]]]]


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





2007-05-02