Definitions
General
The hyperbolic secant function is defined as:
The graph of the hyperbolic secant function is shown in the figure below.
![sech-graph](https://cdn.calcresource.com/images/eval-sech-defines-graph.rev.b8466a1830.png)
Series
All hyperbolic functions can be defined in an infinite series form. Hyperbolic secant function can be written as:
The above series converges for . En 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