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Zapiski Nauchnykh Seminarov LOMI, 1976, Volume 62, Pages 220–233 (Mi znsl2048)  
Asymptotics of solutions of second-order differential equations with two turning points and a complex parameter. I

Z. A. Yanson
Full-text PDF (642 kB)
Abstract: Asymptotic representations are obtained for the solutions of a second-order linear differential equation with coefficient having finite smoothness and containing a complex parameter $\zeta$. The asymptotic solutions are expressed in terms of parabolic cylinder functions, and the estimate for the correction to the leading term of the asymptotic expression is uniform with respect to $\arg\zeta$.
English version:
Journal of Soviet Mathematics, 1979, Volume 11, Issue 5, Pages 804–814
DOI: https://doi.org/10.1007/BF01455060
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: Z. A. Yanson, “Asymptotics of solutions of second-order differential equations with two turning points and a complex parameter. I”, Mathematical problems in the theory of wave propagation. Part 8, Zap. Nauchn. Sem. LOMI, 62, "Nauka", Leningrad. Otdel., Leningrad, 1976, 220–233; J. Soviet Math., 11:5 (1979), 804–814
Citation in format AMSBIB
\Bibitem{Yan76}
\by Z.~A.~Yanson
\paper Asymptotics of solutions of second-order differential equations with two turning points and a complex parameter.~I
\inbook Mathematical problems in the theory of wave propagation. Part~8
\serial Zap. Nauchn. Sem. LOMI
\yr 1976
\vol 62
\pages 220--233
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2048}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=486875}
\zmath{https://zbmath.org/?q=an:0401.34049|0338.34058}
\transl
\jour J. Soviet Math.
\yr 1979
\vol 11
\issue 5
\pages 804--814
\crossref{https://doi.org/10.1007/BF01455060}
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