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Mat. Zametki, 2002, Volume 72, Issue 1, Pages 74–83 (Mi mz405)  

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.

DOI: https://doi.org/10.4213/mzm405

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

Bibliographic databases:

UDC: 517.587
Received: 13.03.2001
Revised: 25.07.2001

Citation: R. S. Larionchikov, “The Plancherel–Rotach Formula for Chebyshev–Hermite Functions on Half-Intervals Contracting to Infinity”, Mat. Zametki, 72:1 (2002), 74–83; Math. Notes, 72:1 (2002), 66–74

Citation in format AMSBIB
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