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Cot




Mathematica Notation

Traditional Notation









Elementary Functions > Cot[z] > Representations through equivalent functions > With related functions > Involving sinh





http://functions.wolfram.com/01.09.27.0049.01









  


  








Input Form





Cot[z] == I (Sqrt[1 + Sinh[I z]^2]/Sinh[I z]) /; Abs[Re[z]] < Pi/2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cot", "[", "z", "]"]], "\[Equal]", RowBox[List["\[ImaginaryI]", FractionBox[SqrtBox[RowBox[List["1", "+", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "2"]]]], RowBox[List["Sinh", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Re", "[", "z", "]"]], "]"]], "<", FractionBox["\[Pi]", "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> <mi> cot </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <msup> <mi> sinh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <cot /> <ci> z </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <sinh /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <sinh /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <lt /> <apply> <abs /> <apply> <real /> <ci> z </ci> </apply> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cot", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["1", "+", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "2"]]]]]], RowBox[List["Sinh", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Re", "[", "z", "]"]], "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]]]


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





2001-10-29