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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 426, Pages 203–217 (Mi znsl6038)  
This article is cited in 5 scientific papers (total in 5 papers)

Some relations between the spheroidal and spherical wave functions

V. G. Farafonova, N. V. Voshchinnikov, E. G. Semenovaa

a St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia
Full-text PDF (199 kB) Citations (5)
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Abstract: We find new relations between the spheroidal and spherical wave functions as well as between the spheroidal functions related to different spheroidal coordinate systems. The systems should have a common origin of coordinate and a common symmetry axis of coordinate surfaces. The applicability ranges of the relations obtained are discussed. Numerical test calculations have demonstrated the high efficiency of the relations in particular those for wave functions including the radial functions of the first kind. As a particular case we consider the relations between the prolate and oblate spheroidal wave functions including the radial functions of the first and second kinds. These relations are necessary to solve the light scattering problem for nonconfocal layered spheroidal particles.
Key words and phrases: spheroidal functions, light scattering, layered nonconfocal spheroids.
Received: 23.09.2014
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 214, Issue 3, Pages 382–391
DOI: https://doi.org/10.1007/s10958-016-2784-3
Bibliographic databases:
Document Type: Article
UDC: 518.3+535.36
Language: Russian
Citation: V. G. Farafonov, N. V. Voshchinnikov, E. G. Semenova, “Some relations between the spheroidal and spherical wave functions”, Mathematical problems in the theory of wave propagation. Part 44, Zap. Nauchn. Sem. POMI, 426, POMI, St. Petersburg, 2014, 203–217; J. Math. Sci. (N. Y.), 214:3 (2016), 382–391
Citation in format AMSBIB
\Bibitem{FarVosSem14}
\by V.~G.~Farafonov, N.~V.~Voshchinnikov, E.~G.~Semenova
\paper Some relations between the spheroidal and spherical wave functions
\inbook Mathematical problems in the theory of wave propagation. Part~44
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 426
\pages 203--217
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6038}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3485312}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 214
\issue 3
\pages 382--391
\crossref{https://doi.org/10.1007/s10958-016-2784-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960426334}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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