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variants of this functions
UnitStep




Mathematica Notation

Traditional Notation









Generalized Functions > UnitStep[x] > Representations through equivalent functions





http://functions.wolfram.com/14.01.27.0003.01









  


  








Input Form





UnitStep[x] == HeavisideTheta[Subscript[x, 1], Subscript[x, 2], \[Ellipsis], Subscript[x, n]] /; Inequality[Subscript[x, 1], Equal, x, Unequal, 0] && n == 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "\[Equal]", RowBox[List["HeavisideTheta", "[", RowBox[List[SubscriptBox["x", "1"], ",", SubscriptBox["x", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["x", "n"]]], "]"]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["x", "1"], "\[Equal]", "x", "\[NotEqual]", "0"]], "\[And]", RowBox[List["n", "\[Equal]", "1"]]]]]]]]








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> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> HeavisideTheta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> x </mi> <mi> n </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <mi> x </mi> <mo> &#8800; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#63449; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> UnitStep </ci> <ci> x </ci> </apply> <apply> <ci> HeavisideTheta </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <ci> n </ci> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Inequality </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <eq /> <ci> x </ci> <neq /> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["UnitStep", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["HeavisideTheta", "[", RowBox[List[SubscriptBox["xx", "1"], ",", SubscriptBox["xx", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["xx", "n"]]], "]"]], "/;", RowBox[List[RowBox[List[SubscriptBox["xx", "1"], "\[Equal]", "x", "\[NotEqual]", "0"]], "&&", RowBox[List["n", "\[Equal]", "1"]]]]]]]]]]


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





2007-05-02