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Elementary Functions > Sech[z] > Introduction to the Hyperbolic Secant Function

Defining the hyperbolic secant function

The hyperbolic secant function is an old mathematical function.

This function is easily defined as the ratio of one and hyperbolic cosine functions:

After comparison with the famous Euler formula for the cosine function , it is easy to derive the following representation of the hyperbolic secant through the circular secant:

The previous formula allows establishment of all the properties and formulas for the hyperbolic secant from corresponding properties and formulas for the circular secant.