Sobre los polinomios generales de Pollaczek

Abstract

Pollaczek general polynomials are a family of orthogonal polynomials with some remarkable properties. In the development of the text, these are expressed in terms of polynomials with leading coefficient equal to one also its recurrence relation is expressed in terms of a continued fraction of Stieltjes and a small implementation is presented in a mathematical software to calculate the general Nth polynomial. A theoretical synthesis of the following topics are presents: Infinite products, Gamma function, continued fraction and other elements of the general theory of orthogonal polynomials; some conclusions and finally the references.