On the power series coefficients of the Riemann zeta function
type: Item
instance of: scholarly article
title: On the power series coefficients of the Riemann zeta function
zbMATH Open document ID: 0683.10032
author: Yasushi Matsuoka
published in: Tokyo Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let \(\gamma_ n=\lim_{N\to \infty}(\sum^{N}_{k=1}\frac{\log^ nk}{k}-\frac{\log^{n+1}N}{n+1})\) be the n-th coefficient of the Laurent expansion of \(\zeta\) (s) at \(s=1\), namely \[ \zeta (s)=\frac{1}{s- 1}+\sum^{\infty}_{n=0}\frac{(-1)^ n}{n!}\gamma_ n(s-1)^ n. \] The author obtains an explicit asymptotic expansion of \(\gamma_ n\), too complicated to be reproduced here.
reviewed by: Aleksandar Ivić
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 4118454
zbMATH Keywords: Riemann zeta function
zbMATH Keywords: gamma-function
zbMATH Keywords: generalized Euler constants
zbMATH Keywords: Laurent expansion
zbMATH Keywords: explicit asymptotic expansion
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270133547
OpenAlex ID: W2070671678
DOI: 10.3836/TJM/1270133547
description: scientific article; zbMATH DE number 4118454