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Search: All articles in the CJM digital archive with keyword Al-Salam-Chihara polynomials

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1. CJM 2002 (vol 54 pp. 709)

Ismail, Mourad E. H.; Stanton, Dennis
$q$-Integral and Moment Representations for $q$-Orthogonal Polynomials
We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for $q$-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the $q$-exponential function $\mathcal{E}_q$.

Keywords:$q$-integral, $q$-orthogonal polynomials, associated polynomials, $q$-difference equations, generating functions, Al-Salam-Chihara polynomials, continuous $q$-ultraspherical polynomials
Categories:33D45, 33D20, 33C45, 30E05

2. CJM 1997 (vol 49 pp. 543)

Ismail, Mourad E. H.; Rahman, Mizan; Suslov, Sergei K.
Some summation theorems and transformations for $q$-series
We introduce a double sum extension of a very well-poised series and extend to this the transformations of Bailey and Sears as well as the ${}_6\f_5$ summation formula of F.~H.~Jackson and the $q$-Dixon sum. We also give $q$-integral representations of the double sum. Generalizations of the Nassrallah-Rahman integral are also found.

Keywords:Basic hypergeometric series, balanced series,, very well-poised series, integral representations,, Al-Salam-Chihara polynomials.
Categories:33D20, 33D60

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