Abstract
Let formula be the Krawtchouk polynomials and µ = N/n. An asymptotic expansion is derived for formula, when x is a fixed number. This expansion holds uniformly for µ in [1, ∞), and is given in terms of the confluent hypergeometric functions. Asymptotic approximations are also obtained for the zeros of formula in various cases depending on the values of p, q and µ. © 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 | 985-1022 |
| 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 first author is partially supported by Liu Bie Ju Center for Mathematics Sciences and by Chinese NNSF grant No. 10271031. The research of the second author is partially supported by grants from the Research Grant Council of Hong Kong.
Research Keywords
- Asymptotic expansions
- Confluent hypergeometric functions
- Krawtchouk polynomials
- Zeros
RGC Funding Information
- RGC-funded
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