A q-Translation Approach to Liu's Calculus

Abstract

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.