(1, 1)-<Emphasis Type="Italic">q</Emphasis>-coherent pairs

In this paper, we introduce the concept of (1, 1)-q-coherent pair of linear functionals (U,V)(\mathcal{U},\mathcal{V}) as the q-analogue to the generalized coherent pair studied by Delgado and Marcellán in (Methods Appl Anal 11(2):273–266, 2004). This means that their corresponding sequences of monic orthogonal polynomials {P _n (x)} _n ≥ 0 and {R _n (x)} _n ≥ 0 satisfy

\frac(DqPn+1)(x)n+1]q + an\frac(DqPn)(x)n]q = Rn(x) + bnRn-1(x)  ,     an 1 0,  n 3 1, \frac{\left(D_qP_{n+1}\right)(x)}{n+1]_q} + a_{n}\frac{\left(D_qP_{n}\right)(x)}{n]_q} = R_{n}(x) + b_{\!n}R_{n-1}(x) \,, \quad\, a_{n}\neq0,\,\, n\geq1,
Keywords:
本文献已被 SpringerLink 等数据库收录！