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# 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

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