We prove a formula for the linearization coefficients of the general Sheffer polynomials, which unifies all the special known results for Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. Furthermore, we give a new and explicit real version of the corresponding formula for Meix
The Combinatorics of Meixner Polynomials: Linearization Coefficients
✍ Scribed by A. de Médicis
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 202 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0195-6698
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✦ Synopsis
We describe various aspects of the Meixner polynomials. These include combinatorial descriptions of the moments, the orthogonality relation, and the linearization coefficients.
📜 SIMILAR VOLUMES
The zeros of the Meixner polynomial m n (x; ;, c) are real, distinct, and lie in (0, ). Let : n, s denote the s th zero of m n (n:; ;, c), counted from the right; and let :Ä n, s denote the sth zero of m n (n:; ;, c), counted from the left. For each fixed s, asymptotic formulas are obtained for both
Let K represent either the real or the complex numbers. Let P k , k=1, 2, ..., r be constant coefficient (with coefficients from K) polynomials in n variables and let r] be the set of all polynomial solutions (of degree M) to this system of partial differential equations. We solve the problem of fi