Convergence of the Fourier Series in Meixner–Sobolev Polynomials and Approximation Properties of Its Partial Sums.

We study the convergence of Fourier series in the polynomial system orthonormal in the sense of Sobolev and generated by the system of modified Meixner polynomials. In particular, we show that the Fourier series of in this system converges to pointwise on the grid as . In addition, we study the approximation properties of partial sums of Fourier series in the system . [ABSTRACT FROM AUTHOR]