  We present a general theory for studying the difference analogues 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.
