Asymptotics and exact formulas for Zagier polynomials

DOI10.1007/s40993-016-0044-8zbMath1396.11100arXiv1506.07612OpenAlexW2474551622MaRDI QIDQ2520563

M. Lawrence Glasser, Atul Dixit, Christophe Vignat, Victor H. Moll

Publication date: 16 December 2016

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.07612

zbMATH Keywords

Chebyshev polynomialsasymptoticsdifferential equationsBernoulli numbersBessel functionsFourier expansionsZagier polynomialsdiffraction theory

Mathematics Subject Classification ID

Approximation by rational functions (41A20) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Irrationality; linear independence over a field (11J72) Matrices, determinants in number theory (11C20)

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Zagier polynomials. II: Arithmetic properties of coefficients
• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• The Zagier modification of Bernoulli numbers and a polynomial extension. I
• Elementary function representations of Schlömilch series
• Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials
• The special functions and their approximations. Vol. I, II
• Schlömilch series that arise in diffraction theory and their efficient computation
• Summation of a Schlömilch type series
• COMPLEX FOURIER--BESSEL TRANSFORMS
• Some recent results on the zeros of Bessel functions and orthogonal polynomials

This page was built for publication: Asymptotics and exact formulas for Zagier polynomials