Difference equations for discrete classical multiple orthogonal polynomials
โ Scribed by D.W. Lee
- Book ID
- 108159041
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 252 KB
- Volume
- 150
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We derive the fourth-order difference equation satisfied by the associated order r of classical orthogonal polynomials of a discrete variable. The coefficients of this equation are given in terms of the polynomials a and z which appear in the discrete Pearson equation A(ap)= zp defining the weight
We prove that if both [P n (x)] n=0 and [{ r P n (x)] n=r are orthogonal polynomials for any fixed integer r 1, then [P n (x)] n=0 must be discrete classical orthogonal polynomials. This result is a discrete version of the classical Hahn's theorem stating that if both [P n (x)] n=0 and [(dรdx) r P n