A new approach to the construction of generalized classical polynomials

  • V. L. Makarov Inst. Math. Acad. Sci. Ukraine, Kiev


UDC 517.587

In this paper, we develop a new method for constructing generalized classical polynomials, primarily 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 such polynomials.
For generalized Hermite polynomials, we investigate a number of properties inherent in classical orthogonal polynomials (orthogonality, generalized Rodrigues formula, three-term recurrence relation forming a function).
The versatility of the method is revealed in constructing generalized Legendre and Chebyshev polynomials of the first kind.


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How to Cite
Makarov, V. L. “A New Approach to the Construction of Generalized Classical Polynomials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 6, June 2021, pp. 827 -38, doi:10.37863/umzh.v73i6.6256.
Research articles