Methods and Applications of Analysis

Volume 11 (2004)

Number 1

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

Pages: 1 – 14

DOI: http://dx.doi.org/10.4310/MAA.2004.v11.n1.a1

Author

Inna Nikolova

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 $p^{'}_{n}(x) = A_{n}(x) p_{n-1}(x) - B_{n}(x) p_{n}(x)$.

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