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Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Discrete case

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

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
712 KB
Volume
87
Category
Article
ISSN
0377-0427

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✦ Synopsis

We present a simple approach in order to compute recursively the connection coefficients between two families of classical (discrete) orthogonal polynomials (Charlier, Meixner, Kravchuk, Hahn), i.e., the coefficients C,.(n) in the expression P.(x) = ~"m=O C,n(n)Q.,(x), where {P.(x)) and {Q,.(x)} belong to the aforementioned class of polynomials. This is done by adapting a general and systematic algorithm, recently developed by the authors, to the discrete classical situation. Moreover, extensions of this method allow to give new addition formulae and to estimate Cm(n)-asymptotics in limit relations between some families.

πŸ“œ SIMILAR VOLUMES

Recurrence relations for the connection
Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable
✍ Stanislaw Lewanowicz πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 575 KB

We give explicitly recurrence relations satisfied by the connection coefficients between two families of the classical orthogonal polynomials of a discrete variable (i.e., associated with the names of Charlier, Meixner, Krawtchouk and Hahn). Also, a recurrence relation is given for the coefficients