Symmetry techniques for q-series: Askey-wilson polynomials

We advocate the exploitation of symmetry (recurrence relation) techniques for the derivation of properties associated with families of basic hypergeometric functions, in analogy with the local Lie theory techniques for ordinary hypergeometric functions. Here these ideas are applied to the (continuous) Askey-Wilson polynomials, introduced by Askey and Wilson, to obtain a strikingly simple derivation of their orthogonality relations.