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Matematicheskie Zametki, 2023, Volume 113, Issue 3, Pages 423–439
DOI: https://doi.org/10.4213/mzm13590 (Mi mzm13590) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On Polynomials Defined by the Discrete Rodrigues Formula

V. N. Sorokinab

a Lomonosov Moscow State University
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
Full-text PDF (600 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm13590
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.
Keywords: Meixner polynomial, discrete Rodrigues formula, saddle point method, algebraic function, equilibrium problem.
Funding agency Grant number
Russian Science Foundation 19-71-30004
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-283
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).
Received: 26.08.2022
Revised: 29.09.2022
English version:
Mathematical Notes, 2023, Volume 113, Issue 3, Pages 420–433
DOI: https://doi.org/10.1134/S0001434623030112
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 33C45
Language: Russian
Citation: V. N. Sorokin, “On Polynomials Defined by the Discrete Rodrigues Formula”, Mat. Zametki, 113:3 (2023), 423–439; Math. Notes, 113:3 (2023), 420–433
Citation in format AMSBIB
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\by V.~N.~Sorokin
\paper On Polynomials Defined by the Discrete Rodrigues Formula
\jour Mat. Zametki
\yr 2023
\vol 113
\issue 3
\pages 423--439
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\crossref{https://doi.org/10.4213/mzm13590}
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\transl
\jour Math. Notes
\yr 2023
\vol 113
\issue 3
\pages 420--433
\crossref{https://doi.org/10.1134/S0001434623030112}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85160245349}
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    • This publication is cited in the following 2 articles:
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