One of the most important mathematical constants is Euler-Mascheroni constant that is the limit of the sequence --------------------------------  and is denoted by gamma. Some other developed constants known as Euler type constants are introduced in order to generalize the above constant. In the present paper, inspired by the functional sequence derivative of the limit summand of functions (i...

We generalize well-known Catalan-type integrals for Euler’s constant to values of the generalized Euler constant function and its derivatives. Using generating functions appearing in these integral representations, we give new Vacca and Ramanujan-type series for values of the generalized Euler constant function and Addison-type series for values of the generalized Euler constant function and it...

We study the distribution of a family {γ(P)} of generalized Euler constants arising from integers sieved by finite sets of primes P . For P = Pr, the set of the first r primes, γ(Pr)→ exp(−γ) as r →∞. Calculations suggest that γ(Pr) is monotonic in r, but we prove it is not. Also, we show a connection between the distribution of γ(Pr) − exp(−γ) and the Riemann hypothesis.

We define a family {γ(P)} of generalized Euler constants indexed by finite sets of primes P and study their distribution. An apparent monotonicity is investigated.