A $q$-linear analogue of the plane wave expansion
Mathematical Physics
2025-01-03 v1 Functional Analysis
math.MP
Abstract
We obtain a -linear analogue of Gegenbauer's expansion of the plane wave. It is expanded in terms of the little -Gegenbauer polynomials and the \textit{third} Jackson -Bessel function. The result is obtained by using a method based on bilinear biorthogonal expansions.
Keywords
Cite
@article{arxiv.1211.0739,
title = {A $q$-linear analogue of the plane wave expansion},
author = {Luís Daniel Abreu and Óscar Ciaurri and Juan Luis Varona},
journal= {arXiv preprint arXiv:1211.0739},
year = {2025}
}
Comments
12 pages, to appear in Adv. in Appl. Math. arXiv admin note: text overlap with arXiv:0909.0067