Asymptotic iteration method for solving Hahn difference equations

Hahn’s difference operator D_q;wf(x) =(f(qx+w)-f(x))/((q-1)x+w) , q∈ (0,1) , w>0 , x≠ w/(1-q) is used to unify the recently established difference and q -asymptotic iteration methods (DAIM, q AIM). The technique is applied to solve the second-order linear Hahn difference equations. The necessary and sufficient conditions for polynomial solutions are derived and examined for the (q;w) -hypergeometric equation.