On the power series coefficients of the Riemann zeta function
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.
scientific article; zbMATH DE number 4118454