Publication: Expansions in series of orthogonal hypergeometric polynomials
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1998-03-09
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Elsevier
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Abstract
Let us consider an arbitrary hypergeometric polynomial $q_j(x)$ and a set of orthogonal hypergeometric polynomials $\{p_n(x)\}$ in the domain of orthogonality $\Gamma$. Here the expansion coefficients of $x^m$ and $x^mq_j(x),\ m\in{\bf N}_0$, in series of the set $\{p_n(x)\}$ are found in terms of the polynomials $\sigma(x)$ and $\tau(x)$ characterizing the second-order differential equations satisfied by the hypergeometric polynomials involved. The resulting general expressions, which are given in an explicit and compact form, are used to produce known (for checking) and unknown expansions for various concrete classical orthogonal polynomials.
Description
16 pages, no figures.-- MSC1991 codes: 33C45; 42C05.
MR#: MR1625951 (99i:33012)
Zbl#: Zbl 0944.33011
MR#: MR1625951 (99i:33012)
Zbl#: Zbl 0944.33011
Keywords
Orthogonal polynomials, Hypergeometric differential equation, Expansions of polynomials
Bibliographic citation
Journal of Computational and Applied Mathematics, 1998, vol. 89, n. 1, p. 155-170