In this article, we consider various generalizations of Euler's famous relation\[\gamma = \sum_{n\geq 2} (-1)^n \frac{\zeta(n)}{n}\]linking Euler's constant $\gamma$ to special values of the Riemann zeta function at positive integers. Among other things, we highlight the existence of a very similar relation for the Apostol-Vu harmonic zeta function which have never been noticed before.
Publié le : 2018-10-29
Classification:
Euler's constant,
first Stieltjes constant,
Riemann zeta function,
har-monic zeta function,
Stirling numbers,
Bernoulli numbers,
Bernoulli numbers of the second kind,
harmonic numbers,
multiple zeta values,
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
@article{hal-01735381,
author = {Coppo, Marc-Antoine},
title = {On certain alternating series involving zeta and multiple zeta values},
journal = {HAL},
volume = {2018},
number = {0},
year = {2018},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01735381}
}
Coppo, Marc-Antoine. On certain alternating series involving zeta and multiple zeta values. HAL, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/hal-01735381/