Is the recurrence relation for orthogonal polynomials always stable?
β Scribed by Walter Gautschi
- Publisher
- Springer Netherlands
- Year
- 1993
- Tongue
- English
- Weight
- 462 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0006-3835
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π SIMILAR VOLUMES
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
One considers the recurrence relation of orthogonal polynomials related to weights |t| A (1 + t 2r /c 2r ) -B on the whole real line, for various integer exponents 2r, and real A > -1, B > 0.
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