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http://functions.wolfram.com/01.09.19.0009.01
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Abs[Cot[z]] == Sqrt[-((Cos[2 Re[z]] + Cosh[2 Im[z]])/
(Cos[2 Re[z]] - Cosh[2 Im[z]]))]
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Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Cot", "[", "z", "]"]], "]"]], "\[Equal]", SqrtBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["Cos", "[", RowBox[List["2", " ", RowBox[List["Re", "[", "z", "]"]]]], "]"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", RowBox[List["Im", "[", "z", "]"]]]], "]"]]]], RowBox[List[RowBox[List["Cos", "[", RowBox[List["2", " ", RowBox[List["Re", "[", "z", "]"]]]], "]"]], "-", RowBox[List["Cosh", "[", RowBox[List["2", " ", RowBox[List["Im", "[", "z", "]"]]]], "]"]]]]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mrow> <mi> cot </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ⩵ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <apply> <cot /> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <real /> <ci> z </ci> </apply> </apply> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <imaginary /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <real /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <imaginary /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", RowBox[List["Cot", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", SqrtBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["Cos", "[", RowBox[List["2", " ", RowBox[List["Re", "[", "z", "]"]]]], "]"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", RowBox[List["Im", "[", "z", "]"]]]], "]"]]]], RowBox[List[RowBox[List["Cos", "[", RowBox[List["2", " ", RowBox[List["Re", "[", "z", "]"]]]], "]"]], "-", RowBox[List["Cosh", "[", RowBox[List["2", " ", RowBox[List["Im", "[", "z", "]"]]]], "]"]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
