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I would like to evaluate numerically the following expression $$ \left.\left[\dfrac{\partial}{\partial b}G_{2,4}^{4,0}\left(2\left|\begin{smallmatrix}0&\tfrac{1}{2}\\b&b&b&b\end{smallmatrix}\right.\right)\right]\right|_{b=1/2}. $$

However, the straightforward

D[MeijerG[{{}, {0, 1/2}}, {{b, b, b, b}, {}}, 2], b] /. b -> 1/2

returns

Derivative[{{}, {0, 0}}, {{0, 0, 0, 1}, {}}, 0][
       MeijerG][{{}, {0, 1/2}}, {{1/2, 1/2, 1/2, 1/2}, {}}, 2] + 
   Derivative[{{}, {0, 0}}, {{0, 0, 1, 0}, {}}, 0][
       MeijerG][{{}, {0, 1/2}}, {{1/2, 1/2, 1/2, 1/2}, {}}, 2] + 
   Derivative[{{}, {0, 0}}, {{0, 1, 0, 0}, {}}, 0][
       MeijerG][{{}, {0, 1/2}}, {{1/2, 1/2, 1/2, 1/2}, {}}, 2] + 
   Derivative[{{}, {0, 0}}, {{1, 0, 0, 0}, {}}, 0][
       MeijerG][{{}, {0, 1/2}}, {{1/2, 1/2, 1/2, 1/2}, {}}, 2]

Is there a way to get Mathematica actually evaluate the derivative?

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$Version

(*  "11.0.1 for Mac OS X x86 (64-bit) (September 21, 2016)"  *)

For a numerical approximation use ND

Needs["NumericalCalculus`"]

ND[MeijerG[{{}, {0, 1/2}}, {{b, b, b, b}, {}}, 2], b, 1/2]

(*  0.0680074  *)
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  • $\begingroup$ Great, thank you. $\endgroup$
    – Alex
    Oct 21 '16 at 15:49

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