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 Bessel function with the parameter , multiplied by :
Other Bessel functions can also be expressed through cosine functions for similar values of the parameter:
Struve functions can also degenerate into the cosine function for similar values 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 another class of functions—the Mathieu functions:
