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variants of this functions
HeavisideTheta




Mathematica Notation

Traditional Notation









Generalized Functions > HeavisideTheta[x] > Series representations > Residue representations





http://functions.wolfram.com/14.05.06.0004.01









  


  








Input Form





HeavisideTheta[x] == -Residue[1/s/(1 + x)^s, {s, 0}] /; x > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HeavisideTheta", "[", "x", "]"]], "\[Equal]", RowBox[List["-", RowBox[List["Residue", "[", " ", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "x"]], ")"]], RowBox[List["-", "s"]]], FractionBox["1", "s"]]], ",", RowBox[List["{", RowBox[List["s", ",", "0"]], "}"]]]], "]"]]]]]], "/;", RowBox[List["x", ">", "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> <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> <mrow> <msub> <mi> res </mi> <mi> s </mi> </msub> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> &#8290; </mo> <mfrac> <mn> 1 </mn> <mi> s </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> HeavisideTheta </ci> <ci> x </ci> </apply> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> res </ci> <ci> s </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> x </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> s </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <gt /> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HeavisideTheta", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["Residue", "[", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "x"]], ")"]], RowBox[List["-", "s"]]], "s"], ",", RowBox[List["{", RowBox[List["s", ",", "0"]], "}"]]]], "]"]]]], "/;", RowBox[List["x", ">", "0"]]]]]]]]


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





2007-05-02