Asymptotic iteration method for solving Hahn difference equations.

Hahn's difference operator D q ; w f ( x ) = ( f ( q x + 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, qAIM). 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.