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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].

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This is not a general answer, but

  • It is perfectly understandable to me. And I think most seasoned mathematicians will not mistake it for anything else.
  • I would personally usually use the vertical bar for restriction or evaluation, like $$ \left. \frac{\partial J_\nu(x)}{\partial \nu}\right|_{\nu = \frac12} $$ to express what you wrote. But that is just one convention that one sees used sometimes in PDEs and geometry.
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  • $\begingroup$ Is the form $\left.\partial_\nu J_\nu(x)\right|_{\nu=1/2}$ okay as well? $\endgroup$
    – Vladimir Reshetnikov
    Nov 19, 2013 at 18:33
  • $\begingroup$ If I see what you wrote in the comment, I would most likely arrive at the correct conclusion as to what you mean. So in that sense I think it is ok. $\endgroup$
    – Willie Wong
    Nov 20, 2013 at 7:50

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