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Approximation of Mathieu Functions by Parabolic Cylinder Functions

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Abstract

The Mathieu equation with complex coefficients of a special form is considered. Simple nonuniform asymptotics of its solutions in terms of parabolic cylinder functions are constructed.

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Acknowledgments

The author wishes to express gratitude to A. P. Kiselev and A. V. Tsvetkova for their interest in the work and helpful remarks.

Funding

The work was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-287).

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Authors and Affiliations

  1. Saint Petersburg State University, Saint Petersburg, 199304, Russia

    E. A. Zlobina

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  1. E. A. Zlobina
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Correspondence to E. A. Zlobina.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 347–352 https://doi.org/10.4213/mzm13975.

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Zlobina, E.A. Approximation of Mathieu Functions by Parabolic Cylinder Functions. Math Notes 114, 303–307 (2023). https://doi.org/10.1134/S0001434623090031

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  • DOI: https://doi.org/10.1134/S0001434623090031

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