DUAL PROPERTIES OF ORTHOGONAL POLYNOMIALS OF DISCRETE VARIABLES ASSOCIATED WITH THE QUANTUM ALGEBRA Uq (su(2))
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![TABLE 1. The Main Data of the q-Hahn Polynomials h αβ n (x(s), N ) q . h αβ n (x(0), N ; q), x(s) = q 2s ρ(x) q [α(α+2N +2s−3)/2]+β(β+2s−1)/2 Γe q (α + N − s)eΓ q (β + s + 1) e Γ q (N − s)eΓ q (s + 1) σ(s) q α+N +2s (q − q −1 ) 2 [s][α + N − s] τ (s) (q −](https://thumb-us.123doks.com/thumbv2/123dok_es/5819306.146095/15.918.82.813.222.974/table-main-data-hahn-polynomials-αβ-αβ-γe.webp)
![TABLE 2. The Main Data of the Alternative q-Hahn Polynomials e h αβ n (x(s), N ) q e h αβ n (x(0), N ; q), x(s) = q 2s ρ(s) q −s(2N +α+β)−[(N +α)(N −α−3)/2]+(N +β)(N +β+1)/2 e](https://thumb-us.123doks.com/thumbv2/123dok_es/5819306.146095/17.918.110.779.186.997/table-main-data-alternative-hahn-polynomials-αβ-αβ.webp)
![TABLE 3. The Main Data of the q-Dual Hahn Polynomials P n (s) W nc (x(s), a, b) q , x(s) = [s] q [s + 1] q (a, b) [a, b − 1] ρ(s) q −s(s+1) eΓ q [s + a + 1]e Γ q [s + c + 1] e](https://thumb-us.123doks.com/thumbv2/123dok_es/5819306.146095/18.918.167.724.148.773/table-main-data-dual-hahn-polynomials-eγ-γ.webp)
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