No abstract

No abstract

No abstract

No abstract

In [4] the authors proved that a quasi-symmetric orthogonal polynomial sequence {Rn} n≥0 is a Laguerre-Hahn sequence if and only if the component {Pn} n≥0 in its quadratic decomposition is also a Laguerre-Hahn sequence. In this paper and under these conditions, we deduce the class s of the Laguerre-Hahn sequence {Rn} n≥0 . More precisely, if s is the class of {Pn} n≥0 then 2s ≤ s ≤ 2s + 3. On the other hand the polynomial coefficients of the Riccati equation satisfied by the Stieltjes function corresponding to {Rn} n≥0 are given in terms of those of {Pn} n≥0 . As an application, we determine all non-symmetric quasi-symmetric Laguerre-Hahn sequences of class one. Mathematics Subject Classification (2010). Primary 33C45; Secondary 42C05.