Opdam's hypergeometric functions: product formula and convolution structure in dimension 1

Jean-Philippe Anker, Fatma Ayadi, Mohamed Sifi

Let $G_{\lambda }^{(\alpha ,\beta )}$ be the eigenfunctions of the Dunkl-Cherednik operator $T^{(\alpha ,\beta )}$ on $\mathbb{R}$. In this paper we express the product $G_{\lambda }^{(\alpha ,\beta )}(x)G_{\lambda }^{(\alpha ,\beta )}(y)$ as an integ…