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On the q-polynomials in the exponential lattice $x(s)=c_1q +c_3$

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URI: https://hdl.handle.net/10016/6414
ISSN: 1065-2469
DOI: 10.1080/10652469908819236
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q-polynomials_arvesu_itsf_1999.pdf (365.49 KB)
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1999-12
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Taylor & Francis
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Abstract
^aThe main goal of this paper is to continue the study of q-polynomials on non-uniform lattices by using the approach introduced by A. F. Nikiforov and V. B. Uvarov [Akad. Nauk SSSR Inst. Prikl. Mat. Preprint 1983, no. 17, 34 pp.; MR0753537 (86c:39006)]. We consider the q-polynomials on the non-uniform exponential lattice $x(s)=c_1q^s+c_3$ and study some of their properties (differentiation formulas, structure relations, representation in terms of hypergeometric and basic hypergeometric functions, etc.). Special emphasis is given to q-analogues of the Charlier orthogonal polynomials. For these Charlier polynomials we compute the main data, i.e., the coefficients of the three-term recurrence relation, the structure relation, the square of the norm, etc., in the exponential lattices $x(s)=q^s$ and $x(s)=(q^s-1)/(q-1)$, respectively.
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26 pages, no figures.-- MSC1991 code: 33D25.
MR#: MR1771452 (2001b:33022)
Zbl#: Zbl 0956.33009
Keywords
Discrete polynomials, q-polynomials, Basic hypergeometric series, Non-uniform lattices, q-Charlier polynomials
Bibliographic citation
Integral Transforms and Special Functions, 1999, vol. 8, n. 3-4, p. 299-324
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