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math.CA2011★ 3 cited
Dual -1 Hahn polynomials: "classical" polynomials beyond the Leonard duality
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
We introduce the -1 dual Hahn polynomials through an appropriate limit of the dual q-Hahn polynomials. These polynomials are orthogonal on a finite set of discrete point…
math.CA2007★ 4 cited
Generalized Bochner theorem: characterization of the Askey-Wilson polynomials
Luc Vinet, Alexei Zhedanov
Assume that there is a set of monic polynomials satisfying the second-order difference equation $$ A(s) P_n(z(s+1)) + B(s) P_n(z(s)) + C(s) P_n(z(s-1)) = λ_n P_n(z(s)), n=…