Some multilinear generating functions for q-Hermite polynomials

DOI10.1016/0022-247X(89)90365-XzbMath0665.33008OpenAlexW2055390796MaRDI QIDQ1116000

S. H. Smith

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0022-247x(89)90365-x

zbMATH Keywords

q-Hermite polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (23)

Summation formula for generalized discrete $q$-Hermite II polynomials ⋮ New forms of the Cauchy operator and some of their applications ⋮ A recurring \(q\)-integral formula ⋮ \(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials ⋮ Probabilistic proofs of some q-identities ⋮ Bivariate generating functions for Rogers-Szegö polynomials ⋮ q-Difference equations of moment integrals for transformational identities and generating functions ⋮ An expectation formula based on a Maclaurin expansion ⋮ A \(q\)-extension of a partial differential equation and the Hahn polynomials ⋮ A multiple \(q\)-translation formula and its implications ⋮ 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 ⋮ A probabilistic version of Mehler's formula ⋮ Notes on Askey-Roy integral and certain generating functions for \(q\)-polynomials ⋮ A note on moment integrals and some applications ⋮ New proofs of generating functions for Rogers-Szegö polynomials ⋮ Unnamed Item ⋮ \(q\)-integral representation of the Al-Salam-Carlitz polynomials ⋮ q-Difference equations for generalized homogeneousq-operators and certain generating functions ⋮ PROBABILISTIC DERIVATION OF A q-POLYNOMIALS TRANSFORMATION FORMULA ⋮ ALTERNATIVE PROOFS OF GENERATING FUNCTIONS FOR HAHN POLYNOMIALS AND SOME APPLICATIONS

Cites Work

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• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• Generating functions for certain q-orthogonal polynomials
• Some extensions of the Mehler formula
• On the Askey-Wilson and Rogers Polynomials
• Certain Summation Formulae for Basic Hypergeometric Series
• Some Orthogonal q‐Polynomials
• Some Extensions of the Mehler Formula
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
• Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q‐Differenzengleichung. Das q‐Analogon der Laplace‐Transformation
• Transformations of Basic Hypergeometric Functions of any Order
• On the Transformation Theory of Basic Hypergeometric Functions

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