A family of second degree semi-classical forms of class s=1

Let 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 second degree symmetric semi-classical forms (when β0=0) of class s≤1 were determined. In this paper, we determine all the semi-classical forms u(β0) of class s=1, which are also of second degree when β0≠0.