Recurrence Coefficients of a New Generalization of the Meixner Polynomials

We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N+1?? and on the bi-lattice N?(N+1??). 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...

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Bibliographic Details
Published inSymmetry, integrability and geometry, methods and applications Vol. 7; p. 068
Main Author Filipuk, Galina
Format Journal Article
LanguageEnglish
Published Kiev National Academy of Sciences of Ukraine 01.01.2011
National Academy of Science of Ukraine
Subjects
Bäcklund transformations
classical solutions
orthogonal polynomials
Painlevé equations
recurrence coefficients
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Summary:We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N+1?? and on the bi-lattice N?(N+1??). 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 PV. Initial conditions for different lattices can be transformed to the classical solutions of PV with special values of the parameters. We also study one property of the Bäcklund transformation of PV.
ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2011.068