Asymptotics of solutions of second-order differential equations with two turning points and a complex parameter.~I
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 220-233
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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 $\arg\zeta$.
@article{ZNSL_1976_62_a17,
author = {Z. A. Yanson},
title = {Asymptotics of solutions of second-order differential equations with two turning points and a complex {parameter.~I}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {220--233},
publisher = {mathdoc},
volume = {62},
year = {1976},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a17/}
}
TY - JOUR AU - Z. A. Yanson TI - Asymptotics of solutions of second-order differential equations with two turning points and a complex parameter.~I JO - Zapiski Nauchnykh Seminarov POMI PY - 1976 SP - 220 EP - 233 VL - 62 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a17/ LA - ru ID - ZNSL_1976_62_a17 ER -
%0 Journal Article %A Z. A. Yanson %T Asymptotics of solutions of second-order differential equations with two turning points and a complex parameter.~I %J Zapiski Nauchnykh Seminarov POMI %D 1976 %P 220-233 %V 62 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a17/ %G ru %F ZNSL_1976_62_a17
Z. A. Yanson. Asymptotics of solutions of second-order differential equations with two turning points and a complex parameter.~I. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 220-233. http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a17/