Asymptotic form of Bessel functions giving a delta

Question

Is there an asymptotic form of the Bessel functions of the first kind $J_{\frac{n}{2}}(a |\mathbf{x}|)$ with order $\frac{n}{2}$ and argument $a |\mathbf{x}|$ (where $\mathbf{x}$ is a variable in the $n$-dimensional space and $a>0$ is a constant coefficient) such that in the limit of $a\to \infty$ $$\lim_{a\to \infty}\left(\frac{2\pi\, a}{|\mathbf{x}|}\right)^{\frac{n}{2}} J_{\frac{n}{2}}(a |\mathbf{x}|)=(2\pi)^n\, \delta(\mathbf{x})$$ being $\delta(\mathbf{x})$ an $n$-dimensional delta function?