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variants of this functions
HeavisideTheta




Mathematica Notation

Traditional Notation









Generalized Functions > HeavisideTheta[x1,x2,...] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/14.06.26.0001.01









  


  








Input Form





HeavisideTheta[Subscript[x, 1], Subscript[x, 2], \[Ellipsis], Subscript[x, n]] == Product[MeijerG[{{}, {1}}, {{0}, {}}, 1 - Subscript[x, k]], {k, 1, n}] /; Subscript[x, k] < 2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HeavisideTheta", "[", RowBox[List[SubscriptBox["x", "1"], ",", SubscriptBox["x", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["x", "n"]]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "1", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["1", "-", SubscriptBox["x", "k"]]]]], "]"]]]]]], "/;", RowBox[List[SubscriptBox["x", "k"], "<", "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> <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> <mo> &#63449; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> x </mi> <mi> k </mi> </msub> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> </mtr> <mtr> <mtd> <mn> 0 </mn> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;1&quot;]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;0&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;x&quot;, &quot;k&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[TagBox[&quot;1&quot;, MeijerG, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <msub> <mi> x </mi> <mi> k </mi> </msub> <mo> &lt; </mo> <mn> 2 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <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> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='integer'> 1 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> </list> <list /> </list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <ci> Subscript </ci> <ci> x </ci> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HeavisideTheta", "[", RowBox[List[SubscriptBox["x_", "1"], ",", SubscriptBox["x_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["x_", "n_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "1", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["1", "-", SubscriptBox["x", "k"]]]]], "]"]]]], "/;", RowBox[List[SubscriptBox["x", "k"], "<", "2"]]]]]]]]


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





2007-05-02