Meixner polynomials

The Fourier Series of the Meixner Polynomials Orthogonal with Respect to the Sobolev-type Inner Product

Authors: Gadzhimirzaev R. M.

In this paper we consider the system of discrete functions {ϕr,k(x)} ∞ k=0 , which is orthonormal with respect to the Sobolev-type inner product hf, gi = Xr−1 ν=0 ∆ ν f(−r)∆ν g(−r) + X t∈Ωr ∆ r f(t)∆r g(t)µ(t), where µ(t) = q t (1−q), 0 < q < 1. It is shown that the shifted classical Meixner polynomials © M−r k (x + r) ª∞ k=r together with functions n (x+r) [k] k! or−1 k=0 form a complete orthogonal system in the space l2,µ(Ωr) with respect to the Sobolev-type inner product.

Limit Discrete Meixner Series and Their Approximative Properties

Authors: Sultanov E. S.

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.