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Erfc




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfc[z] > Integral transforms > Laplace transforms





http://functions.wolfram.com/06.27.22.0004.01









  


  








Input Form





LaplaceTransform[Erfc[t], t, z] == (1 - E^(z^2/4) Erfc[z/2])/z /; Re[z] > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LaplaceTransform", "[", RowBox[List[RowBox[List["Erfc", "[", "t", "]"]], ",", "t", ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["1", "-", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["z", "2"], "4"]], " ", RowBox[List["Erfc", "[", FractionBox["z", "2"], "]"]]]]]], "z"]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msub> <mi> &#8466; </mi> <mi> t </mi> </msub> <mo> [ </mo> <mrow> <mi> erfc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mi> &#8519; </mi> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mfrac> </msup> <mo> &#8290; </mo> <mrow> <mi> erfc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LaplaceTransform </ci> <apply> <ci> Erfc </ci> <ci> t </ci> </apply> <ci> t </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <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> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Erfc </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <gt /> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaplaceTransform", "[", RowBox[List[RowBox[List["Erfc", "[", "t_", "]"]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["z", "2"], "4"]], " ", RowBox[List["Erfc", "[", FractionBox["z", "2"], "]"]]]]]], "z"], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]


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





2001-10-29