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Traditional Notation

Elementary Functions > Cosh[z] > Introduction to the Hyperbolic Cosine Function

Representation using more general functions

The function is a particular case of more complicated mathematical functions. For example, it is a special case of the generalized hypergeometric function with the parameter at :

It is also a particular case of the modified Bessel function with the parameter , multiplied by :

Other Bessel functions can also be expressed through hyperbolic cosine functions for similar values of the parameter:

Struve functions can also degenerate into the hyperbolic cosine function for a similar value of the parameter:

But the function is also a degenerate case of the doubly periodic Jacobi elliptic functions when their second parameter is equal to or :

Finally, the function is the particular case of one more class of functions—the Mathieu functions:

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