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http://functions.wolfram.com/01.24.16.0031.01
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Sech[a - I b] == (2 Cos[b] Cosh[a] + 2 I Sin[b] Sinh[a])/
(Cos[2 b] + Cosh[2 a])
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Cell[BoxData[RowBox[List[RowBox[List["Sech", "[", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["Cos", "[", "b", "]"]], " ", RowBox[List["Cosh", "[", "a", "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["Sin", "[", "b", "]"]], " ", RowBox[List["Sinh", "[", "a", "]"]]]]]], RowBox[List[RowBox[List["Cos", "[", RowBox[List["2", " ", "b"]], "]"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "a"]], "]"]]]]]]]]]
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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> <mi> sech </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sech /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <cos /> <ci> b </ci> </apply> <apply> <cosh /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <sin /> <ci> b </ci> </apply> <apply> <sinh /> <ci> a </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sech", "[", RowBox[List["a_", "-", RowBox[List["\[ImaginaryI]", " ", "b_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["Cos", "[", "b", "]"]], " ", RowBox[List["Cosh", "[", "a", "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["Sin", "[", "b", "]"]], " ", RowBox[List["Sinh", "[", "a", "]"]]]]]], RowBox[List[RowBox[List["Cos", "[", RowBox[List["2", " ", "b"]], "]"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "a"]], "]"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
