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Asymptotic formulas for parabolic cylindrical functions and Hermite polynomials for large argument values

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Abstract

Expansions in the elgenfunctions of the Sturm-Liouville problem and perturbation expansions are applied to obtain asymptotic formulas for parabolic cylindrical functions and Hermite polynomials for large n. The formulas are compared with previously published formulas and, in particular, a numerical comparison is made for one Hermite polynomial.

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References

  1. A. V. Voznyuk, “Construction of asymptotic solutions for quasilinear equations of a special kind,” in: Applied Problems of Dynamics of Controlled-Discrete Elastic Systems [in Russian], Naukova Dumka, Kiev (1975), pp. 133–162.

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  2. B. M. Levitan and I. S. Sargsyan, Introduction to Spectral Theory [in Russian], Nauka, Moscow (1970).

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  3. G. Szego, Orthogonal Polynomials, AMS, New York (1959).

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Authors and Affiliations

  1. Kiev University, USSR

    A. V. Voznyuk

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  1. A. V. Voznyuk
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Additional information

Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 19–24, 1987.

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Voznyuk, A.V. Asymptotic formulas for parabolic cylindrical functions and Hermite polynomials for large argument values. J Math Sci 66, 2139–2143 (1993). https://doi.org/10.1007/BF01098596

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  • DOI: https://doi.org/10.1007/BF01098596

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