New families of q and (q;p)-Hermite polynomials

Abstract: In this paper, we construct a new family of q-Hermite polynomials denoted by Hn(x,s|q). Main properties and relations are established and proved. In addition, is deduced a sequence of novel polynomials, Ln(. ,.|q), which appear to be connected with well known (q,n)-exponential functions E{q,n}(.), introduced by Ernst in his work entitled: (A New Method for q-calculus, Uppsala Dissertations in Mathematics, Vol. 25, 2002). Relevant results spread in the literature are retrieved as particular cases. Fourier integral transforms are explicitly computed and discussed. A (q;p)-extension of the Hn(x,s|q) is also provided.