FORMULAS FOR THE COMPLETE SERIES EXPANSION OF CERTAIN COMBINATIONS OF ZERO-ORDER BESSEL FUNCTIONS OCCURRING IN COAXIAL AND CYLINDRICAL WAVEGUIDE THEORY

摘要

These Bessel function combinations occur in problems of electromagnetic-wave propagation in regions of-cylindrical geometry, such as coaxial and cylindrical waveguides and cavities, as well as in other branches of physics. In most physical problems, these series converge rapidly so that only the first several terms are needed for a close approximation of the Bessel function combinations. These substitutions greatly simplify the solution of many transcendental equations. From these formulas for the expansion of Bessel function combinations, formulas for combinations of Hankel functions are also obtained.