TY - JOUR
T1 - Global asymptotics of the Hahn polynomials
AU - Lin, Y.
AU - Wong, R.
PY - 2013/5
Y1 - 2013/5
N2 - In this paper, we study the asymptotics of the Hahn polynomials Q n(x; α, β, N) as the degree n grows to infinity, when the parameters α and β are fixed and the ratio of n/N = c is a constant in the interval (0, 1). Uniform asymptotic formulas in terms of Airy functions and elementary functions are obtained for z in three overlapping regions, which together cover the whole complex plane. Our method is based on a modified version of the Riemann-Hilbert approach introduced by Deift and Zhou. © 2013 World Scientific Publishing Company.
AB - In this paper, we study the asymptotics of the Hahn polynomials Q n(x; α, β, N) as the degree n grows to infinity, when the parameters α and β are fixed and the ratio of n/N = c is a constant in the interval (0, 1). Uniform asymptotic formulas in terms of Airy functions and elementary functions are obtained for z in three overlapping regions, which together cover the whole complex plane. Our method is based on a modified version of the Riemann-Hilbert approach introduced by Deift and Zhou. © 2013 World Scientific Publishing Company.
KW - Airy function
KW - Global asymptotics
KW - Hahn polynomials
KW - Riemann-Hilbert problems
UR - http://www.scopus.com/inward/record.url?scp=84877267209&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84877267209&origin=recordpage
U2 - 10.1142/S0219530513500188
DO - 10.1142/S0219530513500188
M3 - RGC 21 - Publication in refereed journal
SN - 0219-5305
VL - 11
JO - Analysis and Applications
JF - Analysis and Applications
IS - 3
M1 - 1350018
ER -