A q-Translation Approach to Liu’s Calculus - Aslan, Hatice; Ismail, Mourad E. H. (Springer Science and Business Media Deutschland GmbH, 2021)
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. © 2021, Springer Nature Switzerland AG.
Keywords: Addition theorems; Askey–Wilson operators; Polynomial expansions; q-Exponential functions; q?1 -Hermite polynomials; Translation operators