Abstract
An infinite asymptotic expansion is derived for the Meixner-Pollaczek polynomials Mn (nα; δ, η) as n → ∞, which holds uniformly for -M ≤ α ≤ 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 formula, denotes its sth zero counted from the left, then for each fxed s, three-term asymptotic approximations are obtained for both αn, s and formula, as n → ∞. © 2016 by World Scientific Publishing Co. Ptc. Ltd.
| Original language | English |
|---|---|
| Title of host publication | Selected Works Of Roderick S. C. Wong, The (In 3 Volumes) |
| Publisher | World Scientific Publishing Co. Pte Ltd |
| Pages | 759-790 |
| ISBN (Print) | 9789814656054 |
| DOIs | |
| Publication status | Published - 5 Aug 2015 |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Funding
The research of the second author (RW) is partially supported by a RGC grant from the University Grant Committee of Hong Kong.
Research Keywords
- Meixner-pollaczek polynomials
- Parabolic cylinder functions
- Uniform asymptotic expansions
- Zeros
RGC Funding Information
- RGC-funded
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