Keywords: asymptotics, parabolic cylinder function.
@article{MZM_2023_114_3_a2,
author = {E. A. Zlobina},
title = {Approximation of {Mathieu} {Functions} by {Parabolic}},
journal = {Matemati\v{c}eskie zametki},
pages = {347--352},
year = {2023},
volume = {114},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a2/}
}
E. A. Zlobina. Approximation of Mathieu Functions by Parabolic. Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 347-352. http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a2/
[1] R. E. Langer, “The solutions of the Mathieu equation with a complex variable and at least one parameter large”, Trans. Amer. Math. Soc., 36:3 (1934), 637–710 | DOI | MR
[2] R. W. McKelvey, “The solutions of second order linear ordinary differential equations about a turning point of order two”, Trans. Amer. Math. Soc., 79 (1955), 103–123 | DOI | MR
[3] A. Sharples, “Uniform asymptotic forms of modified Mathieu functions”, Quart. J. Mech. Appl. Math., 20:3 (1967), 365–380 | DOI | MR
[4] A. Sharples, “Uniform asymptotic expansions of modified Mathieu functions”, J. Reine Angew. Math., 247 (1971), 1–17 | DOI | MR
[5] W. Barret, “Mathieu functions of general order: connection formulae, base functions and asymptotic formulae. I–V”, Philos. Trans. Roy. Soc. London Ser. A, 301 (1981), 75–162 | DOI | MR
[6] D. T. Mark, “Uniform asymptotic approximation of Mathieu functions”, Methods Appl. Anal., 1:2 (1994), 143–168 | DOI | MR
[7] NIST Handbook of Mathematical Functions, eds. F. W. G. Olver, D. W. Lozier, R. F. Boisvert, C. B. Clark, Cambridge Univ. Press, Cambridge, 2010 | MR
[8] E. A. Zlobina, A. P. Kiselev, “Frenelevskie perekhodnye zony”, Radiotekhnika i Elektronika, 68:6 (2023), 542–552
[9] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 2, Nauka, M., 1973 | MR
[10] S. Yu. Dobrokhotov, A. V. Tsvetkova, “Global asymptotics for functions of parabolic cylinder and solutions of the Schrödinger equation with a potential in the form of a nonsmooth double well”, Russ. J. Math. Phys., 30:1 (2023), 46–61 | DOI | MR
[11] F. Olver, Vvedenie v asimptoticheskie metody i spetsialnye funktsii, Nauka, M., 1978 | MR