TY - JOUR
T1 - Asymptotic Expansion of the Krawtchouk Polynomials and their Zeros
AU - WONG, Sue Cheun Roderick
AU - Qiu, Weiyuan
PY - 2004/8
Y1 - 2004/8
N2 - Let K N n (x;p,q) KnN(x;p,q)
be the Krawtchouk polynomials and μ = N/n. An asymptotic expansion is derived for K N n (x;p,q) KnN(x;p,q)
, 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 K N n (x;p,q) KnN(x;p,q)
in various cases depending on the values of p, q and μ.
AB - Let K N n (x;p,q) KnN(x;p,q)
be the Krawtchouk polynomials and μ = N/n. An asymptotic expansion is derived for K N n (x;p,q) KnN(x;p,q)
, 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 K N n (x;p,q) KnN(x;p,q)
in various cases depending on the values of p, q and μ.
U2 - 10.1007/BF03321065
DO - 10.1007/BF03321065
M3 - RGC 21 - Publication in refereed journal
SN - 1617-9447
VL - 4
SP - 189
EP - 226
JO - Computational Methods and Function Theory
JF - Computational Methods and Function Theory
IS - 1
ER -