A q-Translation Approach to Liu's Calculus - Aslan, Hatice; Ismail, Mourad E. H. (Springer Basel Ag, 2019)
We show that there is a concept of q-translation behind the approach used by Liu to prove summation and transformation identities for q-series. We revisit the q-translation associated with the Askey-Wilson operator introduced in Ismail (Ann Comb 5(3-4):347-362, 2001), simplify its formalism and point out new properties of this translation operator.
Keywords: Translation operators; Askey-Wilson operators; q-Exponential functions; q-1-Hermite polynomials; Addition theorems; Polynomial expansions; Primary 05A30; 05A40; Secondary 33D45