Inverse operators, \(q\)-fractional integrals, and \(q\)-Bernoulli polynomials

DOI10.1006/jath.2001.3644zbMath0997.33008OpenAlexW1977571797MaRDI QIDQ1604431

Mourad E. H. Ismail, Mizan Rahman

Publication date: 4 July 2002

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.2001.3644

zbMATH Keywords

Askey-Wilson operator\(q\)-Fourier series\(q\)-fractional calculus

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Fractional derivatives and integrals (26A33) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Difference equations, scaling ((q)-differences) (39A13)

Related Items (13)

Asymptotics of zeros of basic sine and cosine functions ⋮ Some identities of \(q\)-Euler polynomials arising from \(q\)-umbral calculus ⋮ \(q\)-fractional calculus for Rubin's \(q\)-difference operator ⋮ \(\lambda\)-\(q\)-Sheffer sequence and its applications ⋮ On a \(q\)-analogue for Bernoulli numbers ⋮ On some questions for the q-integration operator ⋮ \(q\)-fractional integral operators with two parameters ⋮ A new elliptic interpolation formula via the $(f,g)$-inversion ⋮ \(q\)-Bernoulli polynomials and \(q\)-umbral calculus ⋮ A novel approach for obtaining new identities for the lambda extension of q-Euler polynomials arising from the q-umbral calculus ⋮ Duhamel convolution product in the setting of quantum calculus ⋮ \(q\)-type Lidstone expansions and an interpolation problem for entire functions ⋮ \(q\)-fractional Askey-Wilson integrals and related semigroups of operators

Cites Work

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• A Right Inverse of the Askey-Wilson Operator
• A model for the continuous q-ultraspherical polynomials
• Some Fractional q-Integrals and q-Derivatives
• Orthogonality and completeness of \(q\)-Fourier type systems

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