Recursion relations for coefficients in asymptotic expansions of wavefields

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.