New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential
arXiv:math-ph/0607022 · doi:10.1088/0305-4470/39/40/006
Abstract
Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and q-Gegenbauer polynomials in terms of their respective classical analogs.
14 pages