## Methods and Applications of Analysis

- Methods Appl. Anal.
- Volume 11, Number 1 (2004), 001-014.

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

#### Article information

**Source**

Methods Appl. Anal., Volume 11, Number 1 (2004), 001-014.

**Dates**

First available in Project Euclid: 15 June 2005

**Permanent link to this document**

https://projecteuclid.org/euclid.maa/1118850846

**Mathematical Reviews number (MathSciNet)**

MR2128347

**Zentralblatt MATH identifier**

1081.33015

#### Citation

Nikolova, Inna. Difference Equations for Hypergeometric Polynomials from the Askey Scheme. Some Resultants. Discriminants,. Methods Appl. Anal. 11 (2004), no. 1, 001--014. https://projecteuclid.org/euclid.maa/1118850846