The hyperbolic secant is defined as sech z | congruent | 1/(cosh z) | = | 2/(e^z + e^(-z)), where cosh z is the hyperbolic cosine. It is implemented in the Wolfram Language as Sech[z]. On the real line, it has a maximum at x = 0 and inflection points at x = ± cosh^(-1)(sqrt(2)) = 0.881374... (OEIS A091648). It has a fixed point at x = 0.76501... (OEIS A069814).

Benson's formula | catenary | catenoid | Euler number | Gaussian function | hyperbolic cosine | hyperbolic functions | inverse hyperbolic secant | Lorentzian function | oblate spheroidal coordinates | pseudosphere | secant | surface of revolution | tractrix | witch of Agnesi