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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[a,z1,z2] > Series representations > Generalized power series > Expansions at {z1,z2}=={0,0} > For the function itself > Special cases





http://functions.wolfram.com/06.07.06.0012.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "1"]], ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["Log", "[", SubscriptBox["z", "1"], "]"]], "-", RowBox[List["Log", "[", SubscriptBox["z", "2"], "]"]], "+", FractionBox["1", SubscriptBox["z", "1"]], "-", FractionBox[SubscriptBox["z", "1"], "2"], "+", FractionBox[SubsuperscriptBox["z", "1", "2"], "12"], "-", FractionBox[SubsuperscriptBox["z", "1", "3"], "72"], "+", RowBox[List["O", "[", SubsuperscriptBox["z", "1", "4"], "]"]], "-", FractionBox["1", SubscriptBox["z", "2"]], "+", FractionBox[SubscriptBox["z", "2"], "2"], "-", FractionBox[SubsuperscriptBox["z", "2", "2"], "12"], "+", FractionBox[SubsuperscriptBox["z", "2", "3"], "72"], "+", RowBox[List["O", "[", SubsuperscriptBox["z", "2", "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> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mfrac> <mn> 1 </mn> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mfrac> <mo> - </mo> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mn> 12 </mn> </mfrac> <mo> - </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> <mn> 72 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 4 </mn> </msubsup> <mo> ) </mo> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> <mo> + </mo> <mfrac> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mn> 2 </mn> </mfrac> <mo> - </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mn> 12 </mn> </mfrac> <mo> + </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> <mn> 72 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 4 </mn> </msubsup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> Gamma </ci> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <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 /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <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 /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 12 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 72 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <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"]], ",", SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", SubscriptBox["zz", "1"], "]"]], "-", RowBox[List["Log", "[", SubscriptBox["zz", "2"], "]"]], "+", FractionBox["1", SubscriptBox["zz", "1"]], "-", FractionBox[SubscriptBox["zz", "1"], "2"], "+", FractionBox[SubsuperscriptBox["zz", "1", "2"], "12"], "-", FractionBox[SubsuperscriptBox["zz", "1", "3"], "72"], "+", SuperscriptBox[RowBox[List["O", "[", SubscriptBox["zz", "1"], "]"]], "4"], "-", FractionBox["1", SubscriptBox["zz", "2"]], "+", FractionBox[SubscriptBox["zz", "2"], "2"], "-", FractionBox[SubsuperscriptBox["zz", "2", "2"], "12"], "+", FractionBox[SubsuperscriptBox["zz", "2", "3"], "72"], "+", SuperscriptBox[RowBox[List["O", "[", SubscriptBox["zz", "2"], "]"]], "4"]]]]]]]


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





2007-05-02