A family of second degree semi-classical forms of class <Emphasis Type="Italic">s</Emphasis>=1

Let u(β ₀) be the regular form fulfilling (u(β ₀))_2n+1=β ₀(u(β ₀))_2n ,n≥0 where β ₀ is an arbitrary complex number in such a way that for β ₀=0 one has the symmetric forms. Recently, the second degree symmetric semi-classical forms (when β ₀=0) of class s≤1 were determined. In this paper, we determine all the semi-classical forms u(β ₀) of class s=1, which are also of second degree when β ₀≠0.