Hyperbolic cosine integral: Representations through more general functions (formula 01.20.26.0057)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Representations through more general functions

Through other functions

Involving Jacobi functions

http://functions.wolfram.com/01.20.26.0057.01

Input Form

Cosh[z] == 1/JacobiDN[z, 1]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "\[Equal]", FractionBox["1", RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "1"]], "]"]]]]]]]

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> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <cosh /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "1"]], "]"]]]]]]]

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

2001-10-29