Recursion relations for coefficients in asymptotic expansions of wavefields


  • George C. Sherman


Recursion relations satisfied by the coefficients in certain asymptotic expansions of monochromatic wavefields are pointed out and discussed. One of the relations provides a simple means for obtaining higher-order coefficients from a knowledge of the coefficient of the first-order term, and it yields expressions for the coefficients in a very simple form. The utility of that relation is demonstrated by applying it in Sommerfeld's problem of the radiation of an electromagnetic dipole in the presence of a dissipative half-space.