Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions

DOI10.1016/j.jat.2018.06.001zbMath1439.11063arXiv1608.06976OpenAlexW2963348703MaRDI QIDQ1663842

Juan Luis Varona, Óscar Ciaurri, Antonio J. Duran, Mario Pérez Riera

Publication date: 24 August 2018

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

Full work available at URL: https://arxiv.org/abs/1608.06976

zbMATH Keywords

zeros of Bessel functionsDunkl kernelFourier-Dunkl seriesRayleigh functionsApostol-Euler-Dunkl polynomialsAppell-Dunkl sequencesBernoulli-Dunkl polynomials

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Other Dirichlet series and zeta functions (11M41) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (11)

On certain Appell polynomials and their generalizations based on the Tsallis \(q\)-exponential ⋮ Boole-Dunkl polynomials and generalizations ⋮ Some Appell-Dunkl sequences ⋮ On the properties of zeros of Bessel series in the real line ⋮ Discrete Appell-Dunkl sequences and Bernoulli-Dunkl polynomials of the second kind ⋮ Fourier-Dunkl system of the second kind and Euler-Dunkl polynomials ⋮ Bernoulli-Dunkl and Euler-Dunkl polynomials and their generalizations ⋮ Asymptotic behavior of Bernoulli-Dunkl and Euler-Dunkl polynomials and their zeros ⋮ Stirling-Dunkl numbers ⋮ A method for summing Bessel series and a couple of illustrative examples ⋮ Appell-Dunkl sequences and Hurwitz-Dunkl zeta functions

Uses Software

• DLMF

Cites Work

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• On an identity for zeros of Bessel functions
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• Mean convergence of Fourier-Dunkl series
• Nonlocal operational calculi for Dunkl operators
• On the Lerch zeta function
• Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
• On some infinite series involving the zeros of Bessel functions of the first kind
• Differential-Difference Operators Associated to Reflection Groups
• A positive radial product formula for the Dunkl kernel
• A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform
• Some remarks on works concerning the summation of series with inverse powers of zeros of first-kind Bessel functions
• Dunkl–Appelld-orthogonal polynomials
• The Rayleigh Function

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