Asymptotics of extreme zeros of the Meixner-Pollaczek polynomials

摘要

We study the asymptotics of the smallest and largest zeros of the symmetric and asymmetric Meixner-Pollaczek polynomials using two techniques. One is a Coulomb fluid technique developed earlier where the primary input is the weight function. The second uses the method of chain sequences which supplies inequalities for the largest zeros from the knowledge of the recurrence coefficients. An upper bound for the largest zero of Meixner polynomials is also given.