\[\left.\frac{\partial J_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=n}=\frac{%
\pi}{2}Y_{n}\left(z\right)+\frac{n!}{2(\tfrac{1}{2}z)^{n}}\sum_{k=0}^{n-1}%
\frac{(\tfrac{1}{2}z)^{k}J_{k}\left(z\right)}{k!(n-k)}.\]