Orthogonal polynomials on a bi-lattice

Details Orthogonal polynomials on a bi-lattice Orthogonal polynomials on a bi-lattice

2011-01-10

arxiv.org/abs/1101.1817v1

Mathematics

Classical Analysis and ODEs

25 pages, 2 figures

Scientific paper

We investigate generalizations of the Charlier and the Meixner polynomials on the lattice N and on the shifted lattice N+1-\beta. We combine both lattices to obtain the bi-lattice N \cup (N+1-\beta) and show that the orthogonal polynomials on this bi-lattice have recurrence coefficients which satisfy a non-linear system of recurrence equations, which we can identify as a limiting case of an (asymmetric) discrete Painlev\'e equation.

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