Note on the Stieltjes constants: series with Stirling numbers of the first kind
Note on the Stieltjes constants: series with Stirling numbers of the first kind
The Stieltjes constants $��_k(a)$ appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function $��(s,a)$ about $s=1$. We generalize the integral and Stirling number series results of [4] for $��_k(a=1)$. Along the way, we point out another recent asymptotic development for $��_k(a)$ which provides convenient and accurate results for even modest values of $k$.
10 pages, no figures
11M35, 11M06, 11Y60 (Primary), 05A10 (Secondary), Mathematics - Number Theory, Mathematics - Complex Variables, FOS: Mathematics, Number Theory (math.NT), Complex Variables (math.CV)
11M35, 11M06, 11Y60 (Primary), 05A10 (Secondary), Mathematics - Number Theory, Mathematics - Complex Variables, FOS: Mathematics, Number Theory (math.NT), Complex Variables (math.CV)
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!