Name
Abstract | ||
|---|---|---|
It has been recently pointed out that several orthogonal polynomials of the Askey table admit asymptotic expansions in terms of Hermite and Laguerre polynomials [Lopez and Temme, Meth. Appl. Anal. 6 (1999) 131-146; J. Comp. Appl. Math. 133 (2001) 623-633]. From those expansions, several known and new limits between polynomials of the Askey table were obtained in [Lopez and Temme, Meth. Appl. Anal. 6 (1999) 131-146; J. Comp. Appl. Math. 133 (2001) 623-633]. In this paper, we make an exhaustive analysis of the three lower levels of the Askey scheme which completes the asymptotic analysis performed in [Lopez and Temme, Meth. Appl. Anal. 6 (1999) 131-146; J. Comp. Appl. Math. 133 (2001) 623-633]: (i) We obtain asymptotic expansions of Charlier, Meixner-Pollaczek, Jacobi, Meixner, and Krawtchouk polynomials in terms of Hermite polynomials. (ii) We obtain asymptotic expansions of Meixner-Pollaczek, Jacobi, Meixner, and Krawtchouk polynomials in terms of Charlier polynomials. (iii) We give new proofs for the known limits between polynomials of these three levels and derive new limits. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0196-8858(02)00552-3 | Advances in Applied Mathematics |
Keywords | Field | DocType |
asymptotic expansion,charlier polynomial,krawtchouk polynomial,asymptotic analysis,new proof,j. comp,new limit,derive new limit,askey table,asymptotic relation,askey scheme,hypergeometric orthogonal polynomial,laguerre polynomial,orthogonal polynomial,hermite polynomial,classical orthogonal polynomials | Charlier polynomials,Wilson polynomials,Combinatorics,Classical orthogonal polynomials,Orthogonal polynomials,Mathematical analysis,Askey scheme,Discrete orthogonal polynomials,Askey–Wilson polynomials,Hahn polynomials,Mathematics | Journal |
Volume | Issue | ISSN |
31 | 1 | 0196-8858 |
Citations | PageRank | References |
1 | 0.60 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chelo Ferreira | 1 | 8 | 3.01 |
| José L. López | 2 | 25 | 10.53 |
| Esmeralda Mainar | 3 | 150 | 14.27 |