## Definitions

### General

The hyperbolic cosecant function is defined as:

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

### Series

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

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

### Properties

The derivative of the hyperbolic cosecant function is:

The integral of the hyperbolic cosecant is given by:

### Identities