Recurrence Coefficients of a New Generalization of the Meixner Polynomials

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• Main Authors: Filipuk, G., Van Assche, W.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147388
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Recurrence Coefficients of a New Generalization of the Meixner Polynomials / G. Filipuk, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 12 назв. — англ.

We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N+1−β and on the bi-lattice N∪(N+1−β). We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to the solutions of the fifth Painlevé equation...