Prolate spheroidal wave functions of large frequency parameters = and their applications in electromagnetic theory

Maxwell\´s equations in prolate spheroidal coordinates have been separated into three second-order differential equations. These differential equations, satisfied by and , were solved for the frequency parameter c > 10 and the separation constant m = 1, i,e., the uniform circumferential excitations. The asymptotic solutions of the equations for any positive integer m > 1 and c > 10 are given. Thereby, the radiation fields of the metallic prolate spheroid of any length excited by an arbitrary source can be calculated.