\[J_{\nu}'\left(\nu\operatorname{sech}\alpha\right)\sim\left(\frac{\sinh\left(2%
\alpha\right)}{4\pi\nu}\right)^{\frac{1}{2}}e^{\nu(\tanh\alpha-\alpha)}\sum_{k%
=0}^{\infty}\frac{V_{k}(\coth\alpha)}{\nu^{k}},\]