Evaluation of infinite series involving special products and their algebraic characterization

Abstract

ABSTRACT. The aim of the paper is the investigation of special infinite series of the formand {f n (n)} n∈N 0 is a sequence of rational functions. A general summation method for the sum above in the case of the special choice of parameters a, b and f n (n) is included. We find the 2m-tuple of rational numbers α i , β j (1 ≤ i ≤ m, 1 ≤ j ≤ m) for which

A note on the transcendence of infinite products

“…For other applications of the method of Erdős see e.g. [5], [7] or [8]. It seems likely that this method still has great potential.…”

Irrationality of infinite products

“…For other applications of the method of Erdős see e.g. [6], [9], [10] or [11]. It seems that this method still has great potential.…”

Erdős’ Method for Determining the Irrationality of Products

“…Using this idea of Erdős, Hančl et al [8] found some necessary conditions for the Lebesgue measure of E a to be equal to zero in the p-adic case. For other applications of this method see, for instance, [6,7,9,10] or [11]. It seems that Erdős' idea still has great potential.…”