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http://functions.wolfram.com/01.24.16.0029.01
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Sech[a - b] == 1/(Cosh[b] Cosh[a] - Sinh[a] Sinh[b])
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Cell[BoxData[RowBox[List[RowBox[List["Sech", "[", RowBox[List["a", "-", "b"]], "]"]], "\[Equal]", FractionBox["1", RowBox[List[RowBox[List[RowBox[List["Cosh", "[", "b", "]"]], " ", RowBox[List["Cosh", "[", "a", "]"]]]], "-", RowBox[List[RowBox[List["Sinh", "[", "a", "]"]], " ", RowBox[List["Sinh", "[", "b", "]"]]]]]]]]]]]
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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> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mrow> <mi> cosh </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> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </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> <ci> b </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <cosh /> <ci> b </ci> </apply> <apply> <cosh /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <sinh /> <ci> a </ci> </apply> <apply> <sinh /> <ci> b </ci> </apply> </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_", "-", "b_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List[RowBox[List[RowBox[List["Cosh", "[", "b", "]"]], " ", RowBox[List["Cosh", "[", "a", "]"]]]], "-", RowBox[List[RowBox[List["Sinh", "[", "a", "]"]], " ", RowBox[List["Sinh", "[", "b", "]"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
