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A New Approach to the Construction of Generalized Classical Polynomials

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Ukrainian Mathematical Journal Aims and scope

We develop a new method for the construction of generalized classical polynomials (mainly of Hermite polynomials in the sense of A. Krall, J. Koekoek, R. Koekoek, H. Bavinck, L. Littlejohn, et al.). We construct a differential operator of infinite order whose eigenfunctions are polynomials of this kind. For the generalized Hermite polynomials, we analyze various characteristics typical of the classical orthogonal polynomials (such as orthogonality, generalized Rodrigues formula, three-term recurrence relation, and generating function). The universality of the proposed method is demonstrated by constructing generalized Legendre and Chebyshev polynomials of the first kind.

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References

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. L. Makarov

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  1. V. L. Makarov
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Correspondence to V. L. Makarov.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 6, pp. 827–838, June, 2021. Ukrainian DOI: 10.37863/umzh.v73i6.6256.

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Makarov, V.L. A New Approach to the Construction of Generalized Classical Polynomials. Ukr Math J 73, 963–976 (2021). https://doi.org/10.1007/s11253-021-01970-7

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  • DOI: https://doi.org/10.1007/s11253-021-01970-7

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