In this article the problemof function approximation by discrete series by Meixner polynomials orthogonal on uniform net {0, 1, . . .} is investigated. We constructed new series by these polynomials for which partial sums coincidewith input function f(x) in x = 0. These new series were constructed by the passage to the limit of Fourier series Σk=0∞fαkmαk(x) by Meixner polynomials when α → −1.
