Expansions of generalized Euler's constants into the series of polynomials in \(\pi^{- 2}\) and into the formal enveloping series with rational coefficients only

DOI10.1016/j.jnt.2015.06.012zbMath1353.11117arXiv1501.00740OpenAlexW1551970259WikidataQ55878131 ScholiaQ55878131MaRDI QIDQ495307

Iaroslav V. Blagouchine

Publication date: 9 September 2015

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

Full work available at URL: https://arxiv.org/abs/1501.00740

zbMATH Keywords

Stieltjes constantsseries expansionStirling numbersdivergent seriesBernoulli numbersformal seriesharmonic numbersgeneralized Euler's constantsenveloping seriesrational coefficientssemi-convergent series

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) (zeta (s)) and (L(s, chi)) (11M06) Rate of convergence, degree of approximation (41A25) Numerical summation of series (65B10) Evaluation of number-theoretic constants (11Y60)

Related Items (8)

A note on some constants related to the zeta-function and their relationship with the Gregory coefficients ⋮ Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to \(\pi^{-1}\) ⋮ On the Stieltjes constants with respect to harmonic zeta functions ⋮ A generalization of Bohr-Mollerup's theorem for higher order convex functions: a tutorial ⋮ Stieltjes constants appearing in the Laurent expansion of the hyperharmonic zeta function ⋮ Approximating and bounding fractional Stieltjes constants ⋮ Three notes on Ser's and Hasse's representations for the zeta-functions ⋮ On shifted Mascheroni series and hyperharmonic numbers

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