We prove a general formula which, with appropriately chosen parameters, gives a composition formula for squares of Gould–Hopper polynomials g2n(x,h), and hence also for Hermite polynomials. Our main tool is the classical Mehler formula, but with imaginary arguments.
Nous démontrons une formule générale qui, avec des coefficients convenablement choisis, donne une formule de composition pour les carrés des polynômes de Gould–Hopper gn2(x,h) et, par conséquent, pour les carrés des polynômes d'Hermite. Notre outil principal est la formule de Mehler classique avec l'argument imaginaire.
Accepted:
Published online:
@article{CRMATH_2004__338_11_849_0,
author = {Graczyk, Piotr and Nowak, Adam},
title = {A composition formula for squares of {Hermite} polynomials and its generalizations},
journal = {Comptes Rendus. Math\'ematique},
pages = {849--852},
publisher = {Elsevier},
volume = {338},
number = {11},
year = {2004},
doi = {10.1016/j.crma.2003.12.024},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2003.12.024/}
}
TY - JOUR AU - Graczyk, Piotr AU - Nowak, Adam TI - A composition formula for squares of Hermite polynomials and its generalizations JO - Comptes Rendus. Mathématique PY - 2004 SP - 849 EP - 852 VL - 338 IS - 11 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2003.12.024/ DO - 10.1016/j.crma.2003.12.024 LA - en ID - CRMATH_2004__338_11_849_0 ER -
%0 Journal Article %A Graczyk, Piotr %A Nowak, Adam %T A composition formula for squares of Hermite polynomials and its generalizations %J Comptes Rendus. Mathématique %D 2004 %P 849-852 %V 338 %N 11 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2003.12.024/ %R 10.1016/j.crma.2003.12.024 %G en %F CRMATH_2004__338_11_849_0
Graczyk, Piotr; Nowak, Adam. A composition formula for squares of Hermite polynomials and its generalizations. Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 849-852. doi : 10.1016/j.crma.2003.12.024. https://www.numdam.org/articles/10.1016/j.crma.2003.12.024/
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