Chao Min, Yuan Cheng, Yang Chen
Published 2022-09-15Version 1
We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations satisfied by the recurrence coefficients. This allows us to derive the large $n$ asymptotic expansions of the recurrence coefficients. In addition, we also obtain a system of differential-difference equations for the recurrence coefficients.
Asymptotics of recurrence coefficients for the Laguerre weight with a singularity at the edge
Asymptotics of orthogonal polynomials for a weight with a jump on [-1,1]
Differential equations for the recurrence coefficients of semi-classical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach
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