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...

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Veröffentlicht in:	Mathematical Notes 2023-04, Vol.113 (3-4), p.420-433
1. Verfasser:	Sorokin, V. N.
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Sprache:	eng
Schlagworte:	14/34 639/766/189 639/766/530 639/766/747 Mathematics Mathematics and Statistics Meromorphic functions Polynomials Potential theory Riemann surfaces Saddle points
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description	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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title	On Polynomials Defined by the Discrete Rodrigues Formula
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