DUAL PROPERTIES OF ORTHOGONAL POLYNOMIALS OF DISCRETE VARIABLES ASSOCIATED WITH THE QUANTUM ALGEBRA Uq(su(2))
نویسندگان
چکیده
We show that for every set of discrete polynomials yn(x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials zk(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 Uq(su(2)) in terms of various Hahn and Racah q-polynomials.
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