Hyperbolic secant: Transformations (formula 01.24.16.0036)

Sech

$Mathematica Notation$

Elementary Functions

Sech[z]

Transformations

Multiple arguments

Argument involving symbolic multiples of variable

http://functions.wolfram.com/01.24.16.0036.01

Input Form

Sech[n z] == 1/ChebyshevT[n, Cosh[z]]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Sech", "[", RowBox[List["n", " ", "z"]], "]"]], "\[Equal]", FractionBox["1", RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", RowBox[List["Cosh", "[", "z", "]"]]]], "]"]]]]]]]

MathML Form

<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> n </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mn> 1 </mn> <mrow> <msub> <mi> T </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </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>

Rule Form

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", "]"]]]], "]"]]]]]]]

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

2001-10-29