On the Askey-Wilson and Rogers Polynomials
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Publication:3794501
DOI10.4153/CJM-1988-041-0zbMath0649.33005MaRDI QIDQ3794501
Dennis W. Stanton, Mourad E. H. Ismail
Publication date: 1988
Published in: Canadian Journal of Mathematics (Search for Journal in Brave)
Related Items (38)
Probabilistic aspects of Al-Salam–Chihara polynomials ⋮ Extensions of Ramanujan's reciprocity theorem and the Andrews-Askey integral ⋮ The combinatorics of \(q\)-Charlier polynomials ⋮ On classical orthogonal polynomials ⋮ The combinatorics of q-Hermite polynomials and the Askey-Wilson integral ⋮ On sieved orthogonal polynomials. IV. Generating functions ⋮ \(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials ⋮ Some multilinear generating functions for q-Hermite polynomials ⋮ Parameter augmentation for basic hypergeometric series. II ⋮ Bivariate generating functions for Rogers-Szegö polynomials ⋮ Bailey's well-poised \(_{6}\psi _{6}\)-series implies the Askey-Wilson integral ⋮ End of the world brane in double scaled SYK ⋮ A multiple \(q\)-translation formula and its implications ⋮ On Carlitz's trilinear generating functions ⋮ Poisson kernel and multilinear generating functions of some orthogonal polynomials ⋮ Moments for generating functions of Al-Salam-Carlitz polynomials ⋮ Corrigendum to: Some multilinear generating functions for q-Hermite polynomials ⋮ The Askey–Wilson polynomials and q-Sturm–Liouville problems ⋮ Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple \(q\)-series identities ⋮ On integration with respect to the \(q\)-Brownian motion ⋮ \((q,c)\)-derivative operator and its applications ⋮ The Cauchy operator for basic hypergeometric series ⋮ New application of the Cauchy operator on the homogeneous Rogers-Szegö polynomials ⋮ Some expansions in basic Fourier series and related topics ⋮ A note on moment integrals and some applications ⋮ Applications of operator identities to the multiple \(q\)-binomial theorem and \(q\)-Gauss summation theorem ⋮ New proofs of generating functions for Rogers-Szegö polynomials ⋮ Lie algebras and recurrence relations. III: \(q\)-analogs and quantized algebras ⋮ \(q\)-integral representation of the Al-Salam-Carlitz polynomials ⋮ On some limit cases of Askey-Wilson polynomials ⋮ Current research on algebraic combinatorics. Supplements to our book, Algebraic combinatorics I ⋮ An easy proof of the Askey-Wilson integral and applications of the method ⋮ An identity of Andrews and the Askey-Wilson integral ⋮ ALTERNATIVE PROOFS OF GENERATING FUNCTIONS FOR HAHN POLYNOMIALS AND SOME APPLICATIONS ⋮ Two expansion formulas involving the Rogers–Szegő polynomials with applications ⋮ ( q , μ ) and (p,q,ζ)-exponential functions: Rogers–Szegő polynomials and Fourier–Gauss transform ⋮ Interpolation of entire functions, product formula for basic sine function ⋮ Generalizations of Ramanujan's reciprocity formula and the Askey-Wilson integral
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