On Polynomials Defined by the Discrete Rodrigues Formula

We study polynomials given by the discrete Rodrigues formula, which generalizes a similar formula for Meixner polynomials. Such polynomials are associated with the theory of Diophantine approximations. The saddle point method is used to find the limit distribution of zeros of scaled polynomials. An answer is received in terms of a meromorphic function on a compact Riemann surface and is interpreted using the vector equilibrium problem of the logarithmic potential theory.