A large family of Dw-semiclassical polynomials of class one

ABSTRACTLet u(β0) be the regular form fulfilling (u(β0))2n+1=β0(u(β0))2n,n≥0 where β0 is an arbitrary complex number in such a way that for β0=0 one has the symmetric forms. Recently, the symmetric Dw-semiclassical forms (when β0=0) of class s≤1 are determined where Dw is the divided difference operator. In this paper, we determine all the Dw-semiclassical forms u(β0) of class s=1, when β0≠0.