Abstract
We show that for every set of discrete polynomials y n (x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials z k (ξ(t)) of degrees k = s-a and k = b-s-1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative families. This allows us to obtain new expressions for the Clerbsch-Gordan and Racah coefficients of the quantum algebra U q (su(2)) in terms of various Hahn and Racah q-polynomials.
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Dedicated to the memory of our teacher and friend Arnold F. Nikiforov (18.11.1930–27.12.2005).
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Álvarez-Nodarse, R., Smirnov, Y.F. Dual properties of orthogonal polynomials of discrete variables associated with the quantum algebra U q (su(2)). J Russ Laser Res 28, 20–47 (2007). https://doi.org/10.1007/s10946-007-0002-y
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DOI: https://doi.org/10.1007/s10946-007-0002-y