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