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Round




Mathematica Notation

Traditional Notation









Integer Functions > Round[z] > Integral transforms > Fourier cos transforms





http://functions.wolfram.com/04.03.22.0002.01









  


  








Input Form





FourierCosTransform[Round[t], t, z] == (-(1/(Sqrt[2 Pi] z))) Csc[z/2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["FourierCosTransform", "[", RowBox[List[RowBox[List["Round", "[", "t", "]"]], ",", "t", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", "z"]]]]], RowBox[List["Csc", "[", FractionBox["z", "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> <msub> <mi> &#8497;&#119992; </mi> <mi> t </mi> </msub> <mo> [ </mo> <mrow> <mo> &#8970; </mo> <mi> t </mi> <mo> &#8969; </mo> </mrow> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <mi> &#8497;&#119992; </mi> <mi> t </mi> </msub> <mo> [ </mo> <mrow> <mo> &#8970; </mo> <mi> t </mi> <mo> &#8969; </mo> </mrow> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierCosTransform", "[", RowBox[List[RowBox[List["Round", "[", "t_", "]"]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["Csc", "[", FractionBox["z", "2"], "]"]], RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", "z"]]]]]]]]]


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





2001-10-29