Asymptotic behavior and zeros of the Bernoulli polynomials of the second kind

DOI10.1016/j.jat.2020.105517zbMath1478.11029arXiv2011.13808OpenAlexW3112947716MaRDI QIDQ2223566

František Štampach

Publication date: 29 January 2021

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

Full work available at URL: https://arxiv.org/abs/2011.13808

zbMATH Keywords

asymptotic behaviorzerosintegral representationBernoulli polynomials of the second kind

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

Related Items (2)

Asymptotic root distribution of Charlier polynomials with large negative parameter ⋮ Asymptotic behavior of Bernoulli-Dunkl and Euler-Dunkl polynomials and their zeros

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The exact number of real roots of the Bernoulli polynomials
• An explicit formula for Bernoulli polynomials in terms of \(r\)-Stirling numbers of the second kind
• The real zeros of the Bernoulli polynomials
• On the zero attractor of the Euler polynomials
• Large degree asymptotics of generalized Bernoulli and Euler polynomials
• Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials
• An explicit formula for the generalized Bernoulli polynomials
• Bernoulli polynomials of the second kind and general order
• Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum
• On the real zeroes of the Hurwitz zeta-function and Bernoulli polynomials
• Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials
• A note on poly-Bernoulli numbers and polynomials of the second kind
• On the real zeros of Bernoulli polynomials.
• Sur les valeurs asymptotiques des nombres et des polynômes de Bernoulli
• Asymptotic Approximations of Integrals
• A uniform version of Laplace´s method for contour integrals
• A Note on Some Recent Results for the Bernoulli Numbers of the Second Kind
• On multiple zeros of Bernoulli polynomials
• The asymptotics for the number of real roots of the Bernoulli polynomials
• Three notes on Ser's and Hasse's representations for the zeta-functions
• On the Euler and Bernoulli polynomials.

This page was built for publication: Asymptotic behavior and zeros of the Bernoulli polynomials of the second kind