TY - JOUR
T1 - A uniform asymptotic expansion for Krawtchouk polynomials
AU - Li, X.-C.
AU - Wong, R.
PY - 2000/9
Y1 - 2000/9
N2 - 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.
AB - 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.
KW - Krawtchouk polynomials
KW - uniform asymptotic expansion
KW - parabolic cylinder function
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0034258734&origin=recordpage
U2 - 10.1006/jath.2000.3474
DO - 10.1006/jath.2000.3474
M3 - RGC 21 - Publication in refereed journal
SN - 0021-9045
VL - 106
SP - 155
EP - 184
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
IS - 1
ER -