Calculate hyperbolic secant with sech

sech(x) is the reciprocal of hyperbolic cosine: 1 / cosh(x). For real x it is even, equals 1 at zero, and approaches zero as |x| grows.

Relationships

Use cosh for its denominator and tanh for the identity sech(x)^2 + tanh(x)^2 = 1. It appears in localized pulse and probability-shaped models.

Caveats

Unlike sec, sech is hyperbolic rather than circular. Complex inputs can encounter poles where cosh is zero. For exponential expressions, compare exp and take care with extreme values.