Plancherel-Rotach Asymptotic Expansion for Some Polynomials from Indeterminate Moment Problems
Abbreviated Journal Title
Asymptotics; The Chen-Ismail polynomials; The Berg-Letessier-Valent; polynomials; The Conrad-Flajolet polynomials; Turning points; Difference; equation technique; Indeterminate moment problems; Nevanlinna functions; Asymptotics of zeros; Plancherel-Rotach asymptotics; VARYING RECURRENCE COEFFICIENTS; LINEAR DIFFERENCE-EQUATIONS; ORTHOGONAL; POLYNOMIALS; WEIGHTS; RESPECT; Mathematics
We study the Plancherel-Rotach asymptotics of four families of orthogonal polynomials: the Chen-Ismail polynomials, the Berg-Letessier-Valent polynomials, and the Conrad-Flajolet polynomials I and II. All these polynomials arise in indeterminate moment problems, and three of them are birth and death process polynomials with cubic or quartic rates. We employ a difference equation asymptotic technique due to Z. Wang and R. Wong. Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems.
"Plancherel-Rotach Asymptotic Expansion for Some Polynomials from Indeterminate Moment Problems" (2014). Faculty Bibliography 2010s. 5218.