## The electrostatic equilibrium problem for classical discrete orthogonal polynomials

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Przemysław Rutka and Ryszard Smarzewski
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## Abstract:

We present two types of generic difference characterizations of zeros of the classical discrete orthogonal polynomials associated with a discrete weight function satisfying a difference equation of the Pearson type. These characterizations use either the total forward or modified partial central difference operators of discrete discriminants, which approximate the total electrostatic energy of the system of $n$ unit charges moving freely on an interval in presence of external potential given by the iterated discrete weight.## References

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## Additional Information

**Przemysław Rutka**- Affiliation: Institute of Informatics, Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
- MR Author ID: 890344
- ORCID: 0000-0003-4712-2710
- Email: przemyslaw.rutka@mimuw.edu.pl
**Ryszard Smarzewski**- Affiliation: Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, ul. S. Kaliskiego 2, 00-908 Warsaw, Poland
- MR Author ID: 163855
- Email: ryszard.smarzewski@wat.edu.pl
- Received by editor(s): August 26, 2021
- Received by editor(s) in revised form: July 15, 2022, and November 3, 2022
- Published electronically: January 27, 2023
- © Copyright 2023 American Mathematical Society
- Journal: Math. Comp.
**92**(2023), 1331-1348 - MSC (2020): Primary 49M25, 65D20; Secondary 41A10, 33D45
- DOI: https://doi.org/10.1090/mcom/3808
- MathSciNet review: 4550328