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Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable

✍ Scribed by Stanislaw Lewanowicz

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
575 KB
Volume
76
Category
Article
ISSN
0377-0427

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✦ Synopsis

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 in the formula expressing the nth associated polynomial in terms of the original polynomials.

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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)} bel

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