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.
![coth-graph](https://cdn.calcresource.com/images/eval-coth-defines-graph.rev.ab508d69ec.png)
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:
Identities