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There has been renewed interests of classical Nevanlinna theory with respect to difference operator in recent years,mainly due to study of integrability of non-liner difference equations(see Ablowitz,Halburd,Korhonen,etc).We show that there is a deep connection between Nevanlinna theory and Askey-Wilson divided difference operator related to special functions.We use such a function theory to give a new viewpoint on many well-known q-identities involving infinite products and infinite sums.We shall also report on recent development of the Wilson operator when time allows.