A characterization of an Askey-Wilson difference equation

Daniel J. Galiffa; Boon W. Ong

doi:10.1080/10236198.2014.924930

A characterization of an Askey-Wilson difference equation

Daniel J. Galiffa, Boon W. Ong

School of Science (Behrend)

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We determine the q-orthogonal polynomial solutions to the difference equation D_qP_n(X) = γ_nP_n-1(X), where D_q is the Askey-Wilson divided-difference operator, using an approach that does not appear in the literature. To accomplish this, we construct a polynomial expansion via a Chebyshev basis, which ultimately allows explicit formulas to be derived for the recurrence coefficients of P_n(X) above. From there, we obtain our solutions and discuss some future research.

Original language	English (US)
Pages (from-to)	1372-1381
Number of pages	10
Journal	Journal of Difference Equations and Applications
Volume	20
Issue number	9
DOIs	https://doi.org/10.1080/10236198.2014.924930
State	Published - Sep 2014

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1080/10236198.2014.924930

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abstract = "We determine the q-orthogonal polynomial solutions to the difference equation DqPn(X) = γnPn-1(X), where Dq is the Askey-Wilson divided-difference operator, using an approach that does not appear in the literature. To accomplish this, we construct a polynomial expansion via a Chebyshev basis, which ultimately allows explicit formulas to be derived for the recurrence coefficients of Pn(X) above. From there, we obtain our solutions and discuss some future research.",

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AB - We determine the q-orthogonal polynomial solutions to the difference equation DqPn(X) = γnPn-1(X), where Dq is the Askey-Wilson divided-difference operator, using an approach that does not appear in the literature. To accomplish this, we construct a polynomial expansion via a Chebyshev basis, which ultimately allows explicit formulas to be derived for the recurrence coefficients of Pn(X) above. From there, we obtain our solutions and discuss some future research.

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A characterization of an Askey-Wilson difference equation

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