Bessel J in terms of Bessel-Clifford

Theorem

The following formula holds: $$J_n(z) = \left( \dfrac{z}{2} \right)^n \mathcal{C}_n\left( - \dfrac{z^2}{4} \right),$$ where $J_n$ denotes Bessel J and $\mathcal{C}_n$ denotes the Bessel-Clifford function.