Difference Equations for Hypergeometric Polynomials from the Askey Scheme. Some Resultants. Discriminants,

Abstract

It is proven that every sequence from the Askey scheme of hypergeometric polynomials satisfies differentials or difference equations of first order of the form $T p_{n}(x) = A_{n}(x) p_{n-1}(x) - B_{n}(x) p_{n}(x)$, where T is a linear degree reducing operator, which leeds to the fact that these polynomial sets satisfy a relation of the form $p^{'}_{n}(x) = A_{n}(x) p_{n-1}(x) - B_{n}(x) p_{n}(x)$.