The hyperbolic cosine is defined as cosh z congruent 1/2(e^z + e^(-z)). The notation ch x is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). This function describes the shape of a hanging cable, known as the catenary. It is implemented in the Wolfram Language as Cosh[z]. Special values include cosh0 | = | 1 cosh(ln ϕ) | = | 1/2 sqrt(5), where ϕ is the golden ratio.
bipolar coordinates | bipolar cylindrical coordinates | bispherical coordinates | catenary | catenoid | chi | conical function | correlation coefficient--bivariate normal distribution | cosine | cubic equation | de Moivre's identity | elliptic cylindrical coordinates | Elsasser function | hyperbolic functions | hyperbolic geometry | hyperbolic lemniscate function | hyperbolic secant | hyperbolic sine | hyperbolic tangent | inverse hyperbolic cosine | inversive distance | Laplace's equation--bipolar coordinates | Laplace's equation--bispherical coordinates | Laplace's equation--toroidal coordinates | lemniscate function | Lorentz group | Mathieu differential equation | Mehler's Bessel function formula | Mercator projection | modified Bessel function of the first kind | oblate spheroidal coordinates | prolate spheroidal coordinates | pseudosphere | Ramanujan cos/cosh identity | sine-Gordon equation | surface of revolution | toroidal coordinates
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