Poisson kernel and multilinear generating functions of some orthogonal polynomials

DOI10.1016/0022-247X(90)90306-ZzbMath0701.33014MaRDI QIDQ914010

N. E. Zubov

Publication date: 1990

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

q-ultraspherical polynomialsmultilinear generating functionAl-Salam Chihara polynomialsq-random walk polynomials

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (17)

Homogeneous \(q\)-difference equations and generating functions for \(q\)-hypergeometric polynomials ⋮ \(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials ⋮ Generalized homogeneous \(q\)-difference equations for \(q\)-polynomials and their applications to generating functions and fractional \(q\)-integrals ⋮ Bivariate generating functions for Rogers-Szegö polynomials ⋮ q-Difference equations of moment integrals for transformational identities and generating functions ⋮ On a generalized homogeneous Hahn polynomial ⋮ Two \(q\)-operational equations and Hahn polynomials ⋮ On Carlitz's trilinear generating functions ⋮ Moments for generating functions of Al-Salam-Carlitz polynomials ⋮ Generalizations of certain Carlitz's trilinear and Srivastava-Agarwal type generating functions ⋮ Some \(q\)-generating functions of the Carlitz and Srivastava-Agarwal types associated with the generalized Hahn polynomials and the generalized Rogers-Szegö polynomials ⋮ Notes on Askey-Roy integral and certain generating functions for \(q\)-polynomials ⋮ A note on moment integrals and some applications ⋮ Homogeneous \(q\)-partial difference equations and some applications ⋮ New proofs of generating functions for Rogers-Szegö polynomials ⋮ q-Difference equations for generalized homogeneousq-operators and certain generating functions ⋮ ALTERNATIVE PROOFS OF GENERATING FUNCTIONS FOR HAHN POLYNOMIALS AND SOME APPLICATIONS

Cites Work

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• Orthogonal polynomials and some q-beta integrals of Ramanujan
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• q-beta integrals and the q-Hermite polynomials
• Generating functions for certain q-orthogonal polynomials
• Recurrence relations, continued fractions, and orthogonal polynomials
• Positivity of the Poisson Kernel for the Continuous q-Ultraspherical Polynomials
• Rogers’ Linearization Formula for the Continuous q-Ultraspherical Polynomials and Quadratic Transformation Formulas
• On the Askey-Wilson and Rogers Polynomials
• Linearization and Related Formulas for q-Ultraspherical Polynomials
• Certain Summation Formulae for Basic Hypergeometric Series
• Some Orthogonal q‐Polynomials
• SERIES OF HYPERGEOMETRIC TYPE WHICH ARE INFINITE IN BOTH DIRECTIONS
• Transformations of Basic Hypergeometric Functions of any Order
• On the Transformation Theory of Basic Hypergeometric Functions

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