## Hyperbolic cotangent calculator

This tool evaluates the hyperbolic cotangent of a number: coth(x). Enter the argument x below.

 x = Result: coth(x) =

## 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 . Bn denotes the n-th Bernulli number .

### Properties

The derivative of the hyperbolic cotangent function is:

The integral of the hyperbolic cotangent is given by: