Is the notation for values of a derivative at some point that I used in this question commonly accepted and understandable? Is there a more preferred one?
For those who familiar with Mathematica — I used the notation
$$\left[\frac{\partial J_\nu(x)}{\partial\nu}\right]_{\nu=1/2}$$
to represent an equivalent of Mathematica expression Derivative[1, 0][BesselJ][1/2, x]
or, equivalently, Function[ν, BesselJ[ν, x]]'[1/2]
.