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Some symbolic derivatives of certain special functions are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form expression.

Derivative[1, 0][BesselJ][0, 1]
(* Derivative[1, 0][BesselJ][0, 1] *)

(* 1/2 π BesselY[0, x] *)

But for some functions, it takes too much time to evaluate. Possibly, there is even an infinite loop. For example, I left the following expression to evaluate overnight, and it was still running in the morning without any result or messages:

FunctionExpand[Derivative[1, 0][StruveL][0, 1]]

  • Is there a workaround that could get an expanded form of the expression Derivative[1, 0][StruveL][0, 1] in reasonable time?
  • Is there an infinite-loop bug in the implementation of FunctionExpand or do I just have to wait longer for the results (weeks, months, ...)?
  • Is there any public information about what approaches are used by FunctionExpand to expand derivatives?
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See Low-order differentiation here – Dr. belisarius Nov 19 '13 at 1:07
up vote 1 down vote accepted

It seems the current version (10.3) is now aware of the Meijer $G$ expressions for the order derivatives (see this math.SE answer as well):

Derivative[1, 0][StruveL][0, z] // FunctionExpand
   BesselK[0, z] -
   MeijerG[{{1/2, 1/2}, {}}, {{0, 0, 1/2, 1/2}, {}}, z/2, 1/2]/(2 π^2)

(The last version I used, version 8, was unable to do this, if memory serves.)

Nevertheless, FunctionExpand[Derivative[1, 0][StruveL][0, 1]] still takes a ridiculous amount of time (certainly longer than the purely symbolic version); I'm not sure if this is a bug.

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