Four-term recurrence relations of hypergeometric-type polynomials

Abstract

The structural properties of the hypergeometric-type polynomials are, still today, poorly known, except those of the classical orthogonal polynomials (i. e. hypergeometric-type polynomials with Favard's orthogonality) in spite of their great usefulness in Mathematical Physics. Here, we study in detail the four-term recurrence and differential-difference relations of the hypergeometric-type polynomials in terms of the coefficients of its second-order differential equation. In so doing, some results of several authors (Tricomi, Marcellan and others) are considerably extended.