A structure relation for some specific orthogonal polynomials
Abstract
By characterizing all orthogonal polynomials sequences (Pn)n≥ 0 for which (ax+b)( +2\,I)Pn(x(s-1/2))=(an x+bn)Pn(x)+cn Pn-1(x), n=0,1,2,…, where \,I is the identity operator, x defines a q-quadratic lattice, f(s)=f(s+1)-f(s), and (an)n≥0, (bn)n≥0 and (cn)n≥0 are sequences of complex numbers, we derive some new structure relations for some specific families of orthogonal polynomials.
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