Strong Asymptotics for Relativistic Hermite Polynomials

Strong asymptotic results for relativistic Hermite polynomials H N n(z) are established as n, N → ∞, for the cases where N = an + a + 1/2, a > 0, α > -1, or N/n → ∞, thereby supplementing recent results on weak asymptotics for these polynomials. Depending on growth properties of the ratio N/n for the rescaled polynomials H N n(c n z) (c n being suitable positive numbers, n,N → oo), 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.

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