Determination of All Coherent Pairs

✍ Scribed by H.G. Meijer

• Book ID: 102578554
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 362 KB
• Volume: 89
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.3062

✦ Synopsis

A pair of quasi-definite linear functionals [u 0 , u 1 ] on the set of polynomials is called a coherent pair if their corresponding sequences of monic orthogonal polynomials [P n ] and [T n ] satisfy a relation

with _ n non-zero constants. We prove that if [u 0 , u 1 ] is a coherent pair, then at least one of the functionals has to be classical, i.e. Hermite, Laguerre, Jacobi, or Bessel. A similar result is derived for symmetrically coherent pairs.