Premium
Recursion relations for coefficients in asymptotic expansions of wavefields
Author(s) -
Sherman George C.
Publication year - 1973
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs008i008p00811
Subject(s) - recursion (computer science) , simple (philosophy) , mathematics , dissipative system , monochromatic color , mathematical analysis , term (time) , asymptotic expansion , space (punctuation) , physics , optics , quantum mechanics , philosophy , linguistics , epistemology , algorithm
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.