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Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
In this paper, we study a family of orthogonal polynomials
arising from nonlinear coherent states in quantum optics. Based on the
three-term recurrence relation only, we obtain a uniform asymptotic expansion
of as the polynomial degree 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
is provided
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