The \(q\)-Lidstone series involving \(q\)-Bernoulli and \(q\)-Euler polynomials generated by the third Jackson \(q\)-Bessel function

DOI10.1215/21562261-2023-0015arXiv2202.03340OpenAlexW4389239076MaRDI QIDQ6185384

Maryam A. Al-Towailb, Zeinab S. I. Mansour

Publication date: 8 January 2024

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.03340

zbMATH Keywords

\(q\)-Bernoulli polynomials\(q\)-Euler polynomials\(q\)-Lidstone expansion theorem

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Power series (including lacunary series) in one complex variable (30B10) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Difference equations, scaling ((q)-differences) (39A13) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Cites Work

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• Basic Fourier series: convergence on and outside the \(q\)-linear grid
• The \(q\)-tangent and \(q\)-secant numbers via continued fractions
• About the growth of entire functions solutions of linear algebraic \(q\)- difference equations
• On the zeros of the Hahn-Exton \(q\)-Bessel function and associated \(q\)- Lommel polynomials
• \(q\)-lidstone polynomials and existence results for \(q\)-boundary value problems
• On the zeros of the q-analogue exponential function
• The $q$-tangent and $q$-secant numbers via basic Eulerian polynomials
• q-Analogs of Lidstone expansion theorem, two-point Taylor expansion theorem, and Bernoulli polynomials

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