On the asymptotics of the Meixner-Pollaczek polynomials and their zeros
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 59-90 |
| Journal / Publication | Constructive Approximation |
| Volume | 17 |
| Issue number | 1 |
| Publication status | Published - 2001 |
Link(s)
Abstract
An infinite asymptotic expansion is derived for the Meixner-Pollaczek polynomials Mn (nα; δ, η) as n → ∞, which holds uniformly for -M ≤ α ≤ M, where M can be any positive number. This expansion involves the parabolic cylinder function and its derivative. If αn,s denotes the sth zero of Mn(nα; δ, η), counted from the right, and if α̃n,s denotes its sth zero counted from the left, then for each fixed s, three-term asymptotic approximations are obtained for both αn,s and α̃n,s as n → ∞.
Research Area(s)
- Meixner-Pollaczek polynomials, Parabolic cylinder functions, Uniform asymptotic expansions, Zeros
Citation Format(s)
On the asymptotics of the Meixner-Pollaczek polynomials and their zeros. / Li, X.; Wong, R.
In: Constructive Approximation, Vol. 17, No. 1, 2001, p. 59-90.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
