A new product formula involving Bessel functions
A new product formula involving Bessel functions
In this paper, we consider the normalized Bessel function of index $\alpha > -\frac{1}{2}$, we find an integral representation of the term $x^nj_{\alpha+n}(x)j_\alpha(y)$. This allows us to establish a product formula for the generalized Hankel function $B^{\kappa,n}_\lambda$ on $\mathbb{R}$. $B^{\kappa,n}_\lambda$ is the kernel of the integral transform $\mathcal{F}_{\kappa,n}$ arising from …