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 
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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     title = {The {Plancherel{\textendash}Rotach} {Formula} for {Chebyshev{\textendash}Hermite} {Functions} on {Half-Intervals} {Contracting} to {Infinity}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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