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:
