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Angelesco–Meixner polynomials

V. N. Sorokin


Abstract: The polynomials of multiple orthogonality with respect to two discrete Meixner measures on the non-overlapping segments of the real line are considered. The limiting distribution of the zeros of the scaled polynomials is found. The result is obtained in terms of the equilibrium problem of logarithmic potential and in terms of the meromorphic functions on compact Riemann surfaces.

Keywords: Meixner polynomials, logarithmic potential, saddle point method, algebraic functions, Riemann surfaces.

UDC: 517.53

DOI: 10.20948/prepr-2017-27