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Round




Mathematica Notation

Traditional Notation









Integer Functions > Round[z] > Differentiation > Low-order differentiation





http://functions.wolfram.com/04.03.20.0002.01









  


  








Input Form





D[Round[x], x] == Sum[DiracDelta[x - k + 1/2], {k, -Infinity, Infinity}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "x"], RowBox[List["Round", "[", "x", "]"]]]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["DiracDelta", "[", RowBox[List["x", "-", "k", "+", FractionBox["1", "2"]]], " ", "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mo> &#8970; </mo> <mi> x </mi> <mo> &#8969; </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> x </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> <mo> + </mo> <mi> x </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mo> &#8970; </mo> <mi> x </mi> <mo> &#8969; </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> x </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> <mo> + </mo> <mi> x </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["x_"]]], RowBox[List["Round", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["DiracDelta", "[", RowBox[List["x", "-", "k", "+", FractionBox["1", "2"]]], "]"]]]]]]]]


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





2001-10-29