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Classical discrete orthogonal polynomials, Lah numbers, and involutory matrices

✍ Scribed by I. Area; E. Godoy; A. Ronveaux; A. Zarzo

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 225 KB
Volume: 16
Category: Article
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(03)80061-7

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✦ Synopsis

This letter proposes two different approaches in order to solve the connection problems Pn(-X) = fi Cm(n) Pro(x), m=O when the family { Pn (x)} belongs to a wide class of polynomials, including classical discrete orthogonal polynomials. The first approach uses the involutory character of the Lah numbers and of other specific connection coefficients. The second approach presents the recursive Navima algorithm as applied to these problems.

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Limit relations between classical continuous (Jacobi, Laguerre, Hermite) and discrete (Charlier, Meixner, Kravchuk, Hahn) orthogonal polynomials are well known and can be described by relations of type lim;~ P~(x; 2) = Qn(X). Deeper information on these limiting processes can be obtained from the ex