2014/03/27 by Hounkonnou, Mahouton Norbert, Arjika, Sama, Chung, Won Sang
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1403.8080
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 Eq,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.