Relations between spheroidal harmonics and Rayleigh approximation for multilayered nonconfocal spheroids
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 199-242
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The relations between Laplace's spheroidal harmonics related to diffe-\break rent spheroidal coordinates are derived. The transition matrices for the functions of the 1st kind are lower triangular and related by inversion. The matrices for the functions of the 2nd kind are the transposed ones for the functions of the 1st kind. The series for the functions of the 1st kind are finite, and those for the 2nd kind are infinite. In the latter case the region of convergence is considered. Using the derived relations, the rigid solution to the electrostatic problem for the multi-layered scatterers with the non-confocal spheroidal boundaries of the layers is obtained and the Rayleigh approximation is constructed, as well as an approximate approach to a similar light scattering problem that provides reliable results far beyond the range of applicability of the Rayleigh approximation is suggested.
@article{ZNSL_2019_483_a12,
author = {V. G. Farafonov and V. I. Ustimov and V. B. Il'in},
title = {Relations between spheroidal harmonics and {Rayleigh} approximation for multilayered nonconfocal spheroids},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {199--242},
publisher = {mathdoc},
volume = {483},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a12/}
}
TY - JOUR AU - V. G. Farafonov AU - V. I. Ustimov AU - V. B. Il'in TI - Relations between spheroidal harmonics and Rayleigh approximation for multilayered nonconfocal spheroids JO - Zapiski Nauchnykh Seminarov POMI PY - 2019 SP - 199 EP - 242 VL - 483 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a12/ LA - ru ID - ZNSL_2019_483_a12 ER -
%0 Journal Article %A V. G. Farafonov %A V. I. Ustimov %A V. B. Il'in %T Relations between spheroidal harmonics and Rayleigh approximation for multilayered nonconfocal spheroids %J Zapiski Nauchnykh Seminarov POMI %D 2019 %P 199-242 %V 483 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a12/ %G ru %F ZNSL_2019_483_a12
V. G. Farafonov; V. I. Ustimov; V. B. Il'in. Relations between spheroidal harmonics and Rayleigh approximation for multilayered nonconfocal spheroids. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 199-242. http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a12/