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arXiv · 1101.1817

Orthogonal polynomials on a bi-lattice

Christophe Smet·Walter Van Assche
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Abstract

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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Christophe Smet, Walter Van Assche. 2011-01-10. Orthogonal polynomials on a bi-lattice. https://doi.org/10.1007/s00365-011-9145-8

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