Self-similarity and orthogonal polynomials

Some consequences of the analogs of Darboux transformations in the theory o f orthogonal polynomials are considered. In particular, it is shown that se lf-similar closures of the chain of these transformations lead to the so-ca lled semiclassical polynomials. Their simplest representative-modified Char lier polynomials-are considered. These polynomials are orthogonal on an equ idistant lattice without a fixed number of points.