This article is cited in 1 paper

The Plancherel–Rotach Formula for Chebyshev–Hermite Functions on Half-Intervals Contracting to Infinity

R. S. Larionchikov

Moscow Technical University of Communications and Informatics

Abstract: In this paper, we prove the Plancherel–Rotach asymptotic formula for the Chebyshev–Hermite functions $(-1)^ne^{x^2/2}(e^{-x^2})^{(n)}/\sqrt {2^nn!\sqrt \pi}$ and their derivatives for the case in which $+\infty$ belongs to the domain of definition. A method for calculating the approximation accuracy is also given.

UDC: 517.587

Received: 13.03.2001
Revised: 25.07.2001

DOI: 10.4213/mzm405

 English version: Mathematical Notes, 2002, 72:1, 66–74

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