On the properties of special functions on the linear-type lattices

We present a general theory for studying the difference analogs of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particular, using the integral representation of the solutions we obtain several difference–recurrence relations for such functions. Finally, applications to q -classical polynomials are given.