Recurrence coefficients of generalized Meixner polynomials and Painlevé equations

We consider a semi-classical version of the Meixner weight depending on two parameters and the associated set of orthogonal polynomials. These polynomials satisfy a three-term recurrence relation. We show that the coefficients appearing in this relation satisfy a discrete Painleve equation, which is...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2011-01, Vol.44 (3), p.035202-19
Main Authors: Boelen, Lies, Filipuk, Galina, Van Assche, Walter
Format: Article
Language:English
Subjects:
Asymmetry
Constraining
Exact sciences and technology
Functions (mathematics)
Mathematical analysis
Physics
Polynomials
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Summary:We consider a semi-classical version of the Meixner weight depending on two parameters and the associated set of orthogonal polynomials. These polynomials satisfy a three-term recurrence relation. We show that the coefficients appearing in this relation satisfy a discrete Painleve equation, which is a limiting case of an asymmetric dP sub(IV) equation. Moreover, when viewed as functions of one of the parameters, they satisfy one of Chazy's second-degree Painleve equations, which can be reduced to the fifth Painleve equation P sub(V).
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/44/3/035202