Geodesic
The Plancherel--Rotach Formula for Chebyshev--Hermite Functions on Half-Intervals Contracting to Infinity
Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 74-83.

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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. 
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R. S. Larionchikov. The Plancherel--Rotach Formula for Chebyshev--Hermite Functions on Half-Intervals Contracting to Infinity. Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 74-83. http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a6/

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