\[J_{\nu}'\left(z\right)=\frac{(\tfrac{1}{2}z)^{\nu-1}}{2\Gamma\left(\nu\right)}%
\prod_{k=1}^{\infty}\left(1-\frac{z^{2}}{{{j^{\prime}_{\nu,k}}}^{\mspace{-16.0%
mu}2}}\right),\]