Hypergeometric type \(q\)-difference equations: Rodrigues type representation for the second kind solution (Q704175)

In [J. Comput. Appl. Math. 157, 93--106 (2003; Zbl 1036.33005)], the authors considered the so-called hypergeometric type differential equations and obtained a Rodrigues type representation for the general solutions. They also gave indications on how to build similar representations for finite difference analogues. In the present paper, they define and study \(q\)-difference analogues. For these, they obtain Rodrigues type representations. The latter involve \(q\)-integral related to some \(q\)-special functions, for which a general recurrence relation is provided. In this work, the base \(q\) is taken to be real.