Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 005, 6 pages      arXiv:1901.09332     https://doi.org/10.3842/SIGMA.2019.005
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14)

Solution of an Open Problem about Two Families of Orthogonal Polynomials

Walter Van Assche
Department of Mathematics, KU Leuven, Belgium

Received January 18, 2019; Published online January 27, 2019

Abstract
An open problem about two new families of orthogonal polynomials was posed by Alhaidari. Here we will identify one of them as Wilson polynomials. The other family seems to be new but we show that they are discrete orthogonal polynomials on a bounded countable set with one accumulation point at 0 and we give some asymptotics as the degree tends to infinity.

Key words: orthogonal polynomials; special functions; open problems.

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