Product formula for one-dimensional $(k,a)$-generalized Fourier kernel

In this paper, a product formula for the one-dimensional $(k,a)$-generalized Fourier kernel is given for $k\ge 0$, $a>0$ and $2k>a-1$, extending the special case when $a=\frac{2}{n}$, $n\in \mathbb{N}$.