A method for summing Bessel series and a couple of illustrative examples

DOI10.1090/proc/15684zbMath1497.33007OpenAlexW3169075049MaRDI QIDQ5020714

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

Publication date: 7 January 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/15684

zbMATH Keywords

hypergeometric functionsFourier seriesBessel functionsAppell polynomialsBernoulli polynomialsBessel series

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Trigonometric approximation (42A10) Generalized hypergeometric series, ({}_pF_q) (33C20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Möbius inversion formula for Fourier series applied to Bernoulli and Euler polynomials
• On the zero attractor of the Euler polynomials
• Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials
• Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions
• On the summation of Fourier and Bessel series
• Bernoulli-Dunkl and Euler-Dunkl polynomials and their generalizations
• Characterization of Kummer hypergeometric Bernoulli polynomials and applications
• On the Lerch zeta function
• Appell and Sheffer sequences: on their characterizations through functionals and examples
• On the properties of zeros of Bessel series in the real line
• Zeros of Bernoulli, generalized Bernoulli and Euler polynomials
• EVALUATION OF SOME NON-ELEMENTARY INTEGRALS INVOLVING SINE, COSINE, EXPONENTIAL AND LOGARITHMIC INTEGRALS: PART I
• Zeros of the partial sums of \(\cos(z)\) and \(\sin(z)\). I
• Arithmetic properties of Bernoulli-Padé numbers and polynomials.

This page was built for publication: A method for summing Bessel series and a couple of illustrative examples