## Definitions

### General

The hyperbolic secant function is defined as:

The graph of the hyperbolic secant function is shown in the figure below.

### Series

All hyperbolic functions can be defined in an infinite series form. Hyperbolic secant function can be written as:

The above series converges for . E_{n} denotes the n-th Euler number .

### Properties

The derivative of the hyperbolic secant function is:

The integral of the hyperbolic secant is given by:

### Identities