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Ceiling




Mathematica Notation

Traditional Notation









Integer Functions > Ceiling[z] > Representations through equivalent functions > With elementary functions





http://functions.wolfram.com/04.02.27.0008.01









  


  








Input Form





Ceiling[z] == z + ArcTan[Cot[Pi z]]/Pi + 1/2 /; Element[z, Reals] && !Element[z, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", "z", "]"]], "\[Equal]", RowBox[List["z", "+", FractionBox[RowBox[List["ArcTan", "[", RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]], "]"]], "\[Pi]"], "+", FractionBox["1", "2"]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["z", ",", "Reals"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["z", ",", "Integers"]], "]"]], "]"]]]]]]]]








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> <mo> &#8968; </mo> <mi> z </mi> <mo> &#8969; </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> cot </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mi> &#960; </mi> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ceiling /> <ci> z </ci> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <apply> <arctan /> <apply> <cot /> <apply> <times /> <pi /> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <and /> <apply> <in /> <ci> z </ci> <reals /> </apply> <apply> <notin /> <ci> z </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Ceiling", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["z", "+", FractionBox[RowBox[List["ArcTan", "[", RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]], "]"]], "\[Pi]"], "+", FractionBox["1", "2"]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["!", RowBox[List["z", "\[Element]", "Integers"]]]]]]]]]]]]


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





2001-10-29