Representation through more general functions

The hyperbolic cotangent function can be represented using more general mathematical functions. As the ratio of the hyperbolic cosine and sine functions that are particular cases of the generalized hypergeometric, Bessel, Struve, and Mathieu functions, the hyperbolic cotangent function can also be represented as ratios of those special functions. But these representations are not very useful. It is more useful to write the hyperbolic cotangent function as particular cases of one special function. This can be done using doubly periodic Jacobi elliptic functions that degenerate into the hyperbolic cotangent function when their second parameter is equal to or :