There are some known formulae for derivatives of the Bessel functions $J_\nu(x),\,$$Y_\nu(x),\,$$K_\nu(x),\,$$I_\nu(x)\,$with respect to their index $\nu$ for certain values of $\nu$, e.g. $$\left[\frac{\partial J_\nu(x)}{\partial\nu}\right]_{\nu=1/2}=\sqrt{\frac2{\pi\,x}}\Big(\operatorname{Ci}(2\,x)\sin x -\operatorname{Si}(2\,x)\cos x\Big).$$ In this question I am particularly interested in the case $\nu=0$: $$\begin{array}{} &\left[\frac{\partial J_\nu(x)}{\partial\nu}\right]_{\nu=0}=\frac\pi2Y_0(x), &\left[\frac{\partial Y_\nu(x)}{\partial\nu}\right]_{\nu=0}=-\frac\pi2J_0(x),\\ &\left[\frac{\partial K_\nu(x)}{\partial\nu}\right]_{\nu=0}=0, &\left[\frac{\partial I_\nu(x)}{\partial\nu}\right]_{\nu=0}=-K_0(x).\end{array}$$
Are there similar formulae for the Struve functions $\mathbf H_\nu(x)$, $\mathbf L_\nu(x)$, Anger function ${\bf{J}}_\nu(x)$ and Weber function ${\bf{E}}_\nu(x)$?