\(q\)-fractional integral operators with two parameters
DOI10.1016/j.aam.2023.102638arXiv2311.00261OpenAlexW4389041233MaRDI QIDQ6138045
Keru Zhou, Mourad E. H. Ismail
Publication date: 16 January 2024
Published in: Advances in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2311.00261
semigroupsemigroupsAskey-Wilson integralAskey-Wilson polynomialsdivided difference operatorsbilinear generating functionscontinuous \(q\)-Hermite polynomials\(q\)-fractional integral operators
Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Groups and semigroups of linear operators (47D03) Integral operators (45P05) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)
Cites Work
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- \(q\)-Taylor and interpolation series for Jackson \(q\)-difference operators
- Connection relations and bilinear formulas for the classical orthogonal polynomials
- Diagonalization of certain integral operators
- \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions.
- An inverse to the Askey-Wilson operator.
- Inverse operators, \(q\)-fractional integrals, and \(q\)-Bernoulli polynomials
- Applications of \(q\)-Taylor theorems
- \(q\)-fractional Askey-Wilson integrals and related semigroups of operators
- Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
- A Right Inverse of the Askey-Wilson Operator
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