Geodesic
On Polynomials Defined by the Discrete Rodrigues Formula
Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 423-439

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : Meixner polynomial, discrete Rodrigues formula
Keywords: saddle point method, algebraic function, equilibrium problem. 
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     author = {V. N. Sorokin},
     title = {On {Polynomials} {Defined} by the {Discrete} {Rodrigues} {Formula}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {423--439},
     publisher = {mathdoc},
     volume = {113},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a8/}
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V. N. Sorokin. On Polynomials Defined by the Discrete Rodrigues Formula. Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 423-439. http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a8/