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Erfc




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfc[z] > Representations through more general functions > Through other functions





http://functions.wolfram.com/06.27.26.0015.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Erfc", "[", "z", "]"]], "\[Equal]", RowBox[List["1", "-", RowBox[List[FractionBox[RowBox[List[SqrtBox[SuperscriptBox["z", "2"]], " "]], "z"], RowBox[List["(", RowBox[List["1", "-", RowBox[List[FractionBox["1", SqrtBox["\[Pi]"]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]]]], ")"]]]]]]]]]]








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> erfc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mfrac> <mrow> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> <mtext> </mtext> </mrow> <mi> z </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mi> &#960; </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Erfc </ci> <ci> z </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2001-10-29