Abstract:
The theorem on the convergence of a product absolutely and conditionally convergent series, which is defined through the discrete integral in the N.V. Bugaev's sense, was proved. Number-theoretical examples, which illustrate this theorem, are given.
Keywords:absolutely and conditionally convergent series, the Mertens's theorem on a product of series, Bernoulli's polynomials, Riemann's zeta-function.