Strong asymptotics for relativistic Hermite polynomials

Strong asymptotic results for relativistic Hermite polynomials H-n(N) (z) are established as n, N --> infinity, for the cases where N = an + alpha + 1/2, a greater than or equal to 0, alpha > - 1, or N/n --> infinity, thereby supplementing recent results on weak asymptotics for these polynomials. Depending on growth properties of the ratio N/n for the resealed polynomials H-n(N)(c(n)z) (c(n) being suitable positive numbers, n, N --> infinity), formulae of Plancherel-Rotach type are derived on the oscillatory interval, in the complex plane away from the oscillatory region, and near the endpoints of the oscillatory interval.