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

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. 
@article{MZM_2002_72_1_a6,
     author = {R. S. Larionchikov},
     title = {The {Plancherel--Rotach} {Formula} for {Chebyshev--Hermite} {Functions} on {Half-Intervals} {Contracting} to {Infinity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {74--83},
     publisher = {mathdoc},
     volume = {72},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a6/}
}
TY  - JOUR
AU  - R. S. Larionchikov
TI  - The Plancherel--Rotach Formula for Chebyshev--Hermite Functions on Half-Intervals Contracting to Infinity
JO  - Matematičeskie zametki
PY  - 2002
SP  - 74
EP  - 83
VL  - 72
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a6/
LA  - ru
ID  - MZM_2002_72_1_a6
ER  - 
%0 Journal Article
%A R. S. Larionchikov
%T The Plancherel--Rotach Formula for Chebyshev--Hermite Functions on Half-Intervals Contracting to Infinity
%J Matematičeskie zametki
%D 2002
%P 74-83
%V 72
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a6/
%G ru
%F MZM_2002_72_1_a6
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/