Title: A note on some constants related to the zeta-function and their relationship with the Gregory coefficients,
Abstract: In this paper new series for the first and second Stieltjes constants (also
known as generalized Euler's constant), as well as for some closely related
constants are obtained. These series contain rational terms only and involve
the so-called Gregory coefficients, which are also known as (reciprocal)
logarithmic numbers, Cauchy numbers of the first kind and Bernoulli numbers of
the second kind. In addition, two interesting series with rational terms are
given for Euler's constant and the constant ln(2*pi), and yet another
generalization of Euler's constant is proposed and various formulas for the
calculation of these constants are obtained. Finally, in the paper, we mention
that almost all the constants considered in this work admit simple
representations via the Ramanujan summation.