TY - JOUR
T1 - Global asymptotics for Laguerre polynomials with large negative parameter-a Riemann-Hilbert approach
AU - Dai, D.
AU - Wong, R.
PY - 2008/7
Y1 - 2008/7
N2 - In this paper, we study the asymptotic behavior of the Laguerre polynomials Ln(αn)(nz) as n→∞. Here αn is a sequence of negative numbers and -αn/n tends to a limit A>1 as n→∞. An asymptotic expansion is obtained, which is uniformly valid in the upper half plane ℂ+={z: Imz≥0}. A corresponding expansion is also given for the lower half plane ℂ-={z:Imz≥0}. The two expansions hold, in particular, in regions containing the curve Γ in the complex plane, on which these polynomials are orthogonal. Our method is based on the Riemann-Hilbert approach introduced by Deift and Zhou. © 2008 Springer Science+Business Media, LLC.
AB - In this paper, we study the asymptotic behavior of the Laguerre polynomials Ln(αn)(nz) as n→∞. Here αn is a sequence of negative numbers and -αn/n tends to a limit A>1 as n→∞. An asymptotic expansion is obtained, which is uniformly valid in the upper half plane ℂ+={z: Imz≥0}. A corresponding expansion is also given for the lower half plane ℂ-={z:Imz≥0}. The two expansions hold, in particular, in regions containing the curve Γ in the complex plane, on which these polynomials are orthogonal. Our method is based on the Riemann-Hilbert approach introduced by Deift and Zhou. © 2008 Springer Science+Business Media, LLC.
KW - Laguerre polynomials
KW - Riemann-Hilbert problems
KW - Uniform asymptotics
KW - Zeros
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-48349086099&origin=recordpage
U2 - 10.1007/s11139-007-9108-7
DO - 10.1007/s11139-007-9108-7
M3 - RGC 21 - Publication in refereed journal
SN - 1382-4090
VL - 16
SP - 181
EP - 209
JO - Ramanujan Journal
JF - Ramanujan Journal
IS - 2
ER -