Abstract
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.
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Funding
This work was supported by the Moscow Center for Fundamental and Applied Mathematics, agreement with the Ministry of Science and Higher Education of the Russian Federation no. 075-15-2022-283, and by the Russian Science Foundation under grant 19-71-30004 (Sec. 4 in this paper).
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 423–439 https://doi.org/10.4213/mzm13590.
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Sorokin, V.N. On Polynomials Defined by the Discrete Rodrigues Formula. Math Notes 113, 420–433 (2023). https://doi.org/10.1134/S0001434623030112
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DOI: https://doi.org/10.1134/S0001434623030112