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variants of this functions
GammaRegularized




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > GammaRegularized[a,z] > Specific values > Specialized values > For fixed z





http://functions.wolfram.com/06.08.03.0006.01









  


  








Input Form





GammaRegularized[-(1/2), z] == Erfc[Sqrt[z]] - 1/(E^z (Sqrt[Pi] Sqrt[z]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Erfc", "[", SqrtBox["z"], "]"]], "-", FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], RowBox[List[SqrtBox["\[Pi]"], SqrtBox["z"]]]]]]]]]]








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> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> erfc </mi> <mo> &#8289; </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mo> - </mo> <mfrac> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mrow> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> GammaRegularized </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> Erfc </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GammaRegularized", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Erfc", "[", SqrtBox["z"], "]"]], "-", FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox["z"]]]]]]]]]]


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





2001-10-29