TY - JOUR
T1 - Uniform asymptotics of orthogonal polynomials arising from Coherent states
AU - Dai, Dan
AU - Hu, Weiying
AU - Wang, Xiang-Sheng
PY - 2015
Y1 - 2015
N2 - In this paper, we study a family of orthogonal polynomials {φn (z)} arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of φn (z) as the polynomial degree n tends to infinity. Our asymptotic results suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong’s difference equation method. In addition, the limiting zero distribution of the polynomials φn (z) is provided.
AB - In this paper, we study a family of orthogonal polynomials {φn (z)} arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of φn (z) as the polynomial degree n tends to infinity. Our asymptotic results suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong’s difference equation method. In addition, the limiting zero distribution of the polynomials φn (z) is provided.
KW - Coherent states
KW - Orthogonal polynomials
KW - Three-term recurrence relation
KW - Uniform asymptotics
UR - http://www.scopus.com/inward/record.url?scp=84940777821&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84940777821&origin=recordpage
U2 - 10.3842/SIGMA.2015.070
DO - 10.3842/SIGMA.2015.070
M3 - 21_Publication in refereed journal
VL - 11
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
SN - 1815-0659
M1 - A070
ER -