On the Expansion of Bessel Functions in a Series of Mathieu Functions and on a Property of Mathieu Functions

The expansions of Mathieu Functions in terms of Bessel Functions have been investigated by many writers, notable amongst them being Dr. Dhar Dr. J. Dougall and Goldstein, but uptill now no writer has investigated the problem of expressing Bessel Functions in terms of Mathieu Functions. This latter method has its own advantages in as much as, it will enable us to obtain some of the properties of Mathieu Functions.