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variants of this functions
GammaRegularized




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.09.06.0010.01









  


  








Input Form





GammaRegularized[1, Subscript[z, 1], Subscript[z, 2]] \[Proportional] -Subscript[z, 1] + O[Subscript[z, 1]^3] + Subscript[z, 2] + O[Subscript[z, 1]^3]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List["1", ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["-", SubscriptBox["z", "1"]]], "+", RowBox[List["O", "[", SubsuperscriptBox["z", "1", "3"], "]"]], "+", SubscriptBox["z", "2"], "+", RowBox[List["O", "[", SubsuperscriptBox["z", "1", "3"], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mn> 1 </mn> <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> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> <mo> ) </mo> </mrow> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> GammaRegularized </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> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> O </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GammaRegularized", "[", RowBox[List["1", ",", SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SubscriptBox["zz", "1"]]], "+", SuperscriptBox[RowBox[List["O", "[", SubscriptBox["zz", "1"], "]"]], "3"], "+", SubscriptBox["zz", "2"], "+", SuperscriptBox[RowBox[List["O", "[", SubscriptBox["zz", "1"], "]"]], "3"]]]]]]]


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





2007-05-02