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Table of Contents

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## Definitions

### General

The hyperbolic tangent function is defined as:

The graph of the hyperbolic tangent function is shown in the figure below. It is a monotonic function unlike the trigonometric tangent, which is periodic .

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### Series

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

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

From the expanded form of the series it can be seen that the higher terms become insignificant, for values of x close to zero, resulting in the following quite useful approximation:

### Properties

The derivative of the hyperbolic tangent function is:

The integral of the hyperbolic tangent is given by:

### Identities

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