## Definitions

### General

The hyperbolic cotangent function is defined as:

The graph of the hyperbolic cotangent function is shown in the figure below. Unlike the trigonometric cotangent, the function is not periodic.

### Series

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

The above series converges for . B_{n} denotes the n-th Bernulli number .

### Properties

The derivative of the hyperbolic cotangent function is:

The integral of the hyperbolic cotangent is given by:

### Identities