Zhang, Nanyue; Williams, Kenneth S. Some results on the generalized Stieltjes constants. (English) Zbl 0808.11054 Analysis 14, No. 2-3, 147-162 (1994). For \(0<a\leq 1\) and \(\sigma>1\) the Hurwitz zeta function \(\zeta(s,a)\) is defined by \(\zeta(s,a)= \sum_{n=0}^ \infty (n+a)^{-s}\), \(s=\sigma+ it\). \(\zeta(s,a)\) has the Laurent series expansion \[ \zeta(s,a)= {1\over {s-1}}+ \sum_{n=0}^ \infty {{(-1)^ n \nu_ n(a)} \over {n!}} (s- 1)^ n \] where the \(\gamma_ n(a)\) are known as generalized Stieltjes constants. The author proves a number of expressions and estimates for these constants. Reviewer: William E. Briggs (Boulder) Cited in 1 ReviewCited in 24 Documents MSC: 11M35 Hurwitz and Lerch zeta functions Keywords:Hurwitz zeta function; Laurent series expansion; generalized Stieltjes constants PDFBibTeX XMLCite \textit{N. Zhang} and \textit{K. S. Williams}, Analysis 14, No. 2--3, 147--162 (1994; Zbl 0808.11054)