A uniform asymptotic expansion for Krawtchouk polynomials
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
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Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 155-184 |
| Journal / Publication | Journal of Approximation Theory |
| Volume | 106 |
| Issue number | 1 |
| Publication status | Published - Sep 2000 |
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Abstract
We study the asymptotic behavior of the Krawtchouk polynomial K(N)n(x; p, q) as n→∞. With x≡λN and ν=n/N, an infinite asymptotic expansion is derived, which holds uniformly for λ and ν in compact subintervals of (0, 1). This expansion involves the parabolic cylinder function and its derivative. When ν is a fixed number, our result includes the various asymptotic approximations recently given by M. E. H. Ismail and P. Simeonov. © 2000 Academic Press.
Research Area(s)
- Krawtchouk polynomials, uniform asymptotic expansion, parabolic cylinder function
Citation Format(s)
A uniform asymptotic expansion for Krawtchouk polynomials. / Li, X.-C.; Wong, R.
In: Journal of Approximation Theory, Vol. 106, No. 1, 09.2000, p. 155-184.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
