A new approach to the construction of generalized classical polynomials
Abstract
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.
References
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