Sorokin, Vladimir N. 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. Cited in 2 Documents MSC: 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis 41A10 Approximation by polynomials Keywords:Meixner polynomials; discrete Rodrigues formula; Apéry approximations; saddle-point method; algebraic functions; equilibrium problem × Cite Format Result Cite Review PDF Full Text: DOI MNR