An operator calculus for the Askey-Wilson operator

DOI10.1007/s00026-001-8015-7zbMath0988.05016OpenAlexW2074036970MaRDI QIDQ1600819

Mourad E. H. Ismail

Publication date: 16 June 2002

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00026-001-8015-7

zbMATH Keywords

generating functionsSheffer sequences\(q\)-calculusoperator calculus\(q\)-translationcontinuous \(q\)-Hermite polynomials\(q\)-A type zero\(q\)-shift-invariant operatorspolynomials of \(q\)-binomial type

Mathematics Subject Classification ID

Umbral calculus (05A40) (q)-calculus and related topics (05A30) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (5)

Integral representations and holonomic \(q\)-difference structure of Askey-Wilson type functions ⋮ On the \(q\)-translation associated with the Askey-Wilson operator ⋮ On linear dynamics in quantum calculus ⋮ A \(q\)-translation approach to Liu's calculus ⋮ Inverse operators, \(q\)-fractional integrals, and \(q\)-Bernoulli polynomials

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