Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center

Download All Formulas For This Function
Mathematica Notebook
PDF File


Developed with Mathematica -- Download a Free Trial Version

variants of this functions

Mathematica Notation

Traditional Notation

Generalized Functions > HeavisideTheta[x] > Limit representations




Input Form

HeavisideTheta[x] == Limit[1/(1 + Exp[-(x/\[CurlyEpsilon])]), \[CurlyEpsilon] -> Plus[0]]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["HeavisideTheta", "[", "x", "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[FractionBox["1", RowBox[List["1", "+", RowBox[List["Exp", "[", RowBox[List["-", FractionBox["x", "\[CurlyEpsilon]"]]], "]"]]]]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "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> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> HeavisideTheta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> &#949; </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mrow> <mo> + </mo> <mn> 0 </mn> </mrow> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mfrac> <mn> 1 </mn> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <mi> x </mi> <mi> &#949; </mi> </mfrac> </mrow> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HeavisideTheta </ci> <ci> x </ci> </apply> <apply> <limit /> <bvar> <ci> &#949; </ci> </bvar> <condition> <apply> <tendsto /> <ci> &#949; </ci> <apply> <plus /> <cn type='integer'> 0 </cn> </apply> </apply> </condition> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> x </ci> <apply> <power /> <ci> &#949; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HeavisideTheta", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[FractionBox["1", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["x", "\[CurlyEpsilon]"]]]]]]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]]]]]]

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