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A generalization of the discrete Rodrigues formula for Meixner polynomials. (English. Russian original) Zbl 1539.42033

Sb. Math. 213, No. 11, 1559-1581 (2022); translation from Mat. Sb. 213, No. 11, 79-101 (2022).
Summary: A generalization of Meixner polynomials leading to a new construction of Apéry approximations is put forward. The limiting distribution of the zeros of scaled polynomials is described in terms of algebraic functions. The resulting distribution is shown to be a solution of some vector equilibrium problem in the theory of logarithmic potential.

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
41A10 Approximation by polynomials