Asymptotics and weighted estimates of Meixner polynomials orthogonal on the grid \(\{ 0,\delta,2\delta,\dots\}\) (Q1277559)

Meixner polynomials are the discrete analogues to Laguerre orthogonal polynomials. The author proves for Meixner polynomials an asymptotic formula in terms of Laguerre polynomials. The proof uses Euler summation formula and an author's estimate for Stirling numbers [\textit{I. I. Sharapudinov}, Math. Sb. 180, No. 9, 1259-1277 (1989; Zbl 0689.33005)]. As a consequence, the author obtains a weighted estimate for the Meixner polynomials on \([0,+\infty[\) by means of a classical estimate for Laguerre polynomials [\textit{R. Askey} and \textit{S. Wainger}, Am. J. Math. 87, 695-708 (1965; Zbl 0125.31301)].