FULL TRANSLATIONAL ADDITION EXPRESSIONS VIA CYLINDRICAL WAVE-FUNCTIONTRANSFORMATION FOR MATHIEU WAVE-FUNCTIONS

The translational addition theorems of elliptic scalar wave functions are useful for the study of systems of multiple conductors or multiple optical fibers of elliptic cross sections. However, complete and comp rehensive expressions for the elliptic addition theorems are not avala ible in the literature. In this paper these translational addition exp ressions applied to the Mathieu wave functions as well as to the modif ied wave functions are derived in closed form by using a cylindrical w ave-function transformation. This physical-geometric transformation gi ves new insights in the development of the elliptic wave addition expr essions.