Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials
Abbreviated Journal Title
q-Orthogonal polynomials; Asymptotics; Recurrence relations; Ramanujan; function; Error terms; VARYING RECURRENCE COEFFICIENTS; Mathematics
We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q (-1)-Hermite polynomials of Askey, Ismail, and Masson; q-Laguerre polynomials; and the Stieltjes-Wigert polynomials. We also introduce a one-parameter family of solutions to the q-difference equation of the Ramanujan function.
"Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials" (2013). Faculty Bibliography 2010s. 4142.