Some symmetric semi-classical orthogonal polynomials of class 0 ≤ s ≤ 5

The system fulfilled by symmetric semi-classical orthogonal polynomial sequences of class s = 2 is not linear and has not been sorted out. Alaya and Bouras [Alaya, J. and Bouras B., Symmetric semi-classical forms of class s = 2. Integral Transforms and Special Functions , in press.] used Hankel determinants to give only one case of these sequences. In this paper, we present a method which investigates not only this previous case, but also gives new ones of class s >= 2.