Sech[n z] == 1/ChebyshevT[n, Cosh[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> <mi> sech </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 1 </mn> <mrow> <msub> <mi> T </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sech /> <apply> <times /> <ci> n </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> ChebyshevT </ci> <ci> n </ci> <apply> <cosh /> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sech", "[", RowBox[List["n_", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", RowBox[List["Cosh", "[", "z", "]"]]]], "]"]]]]]]]

2001-10-29