On the Properties of Special Functions on the linear-type lattices

Details On the Properties of Special Functions on the linear-type lattices On the Properties of Special Functions on the linear-type lattices

2011-07-29

arxiv.org/abs/1107.5898v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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