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D vs. Derivative

  • To: mathgroup at
  • Subject: [mg15601] D vs. Derivative
  • From: Gianluca Gorni <gorni at>
  • Date: Thu, 28 Jan 1999 04:23:30 -0500 (EST)
  • Sender: owner-wri-mathgroup at


It seems that D[f[x],x] and f'[x] are not equivalent, and the latter can
give useless outputs.

Consider the following power series, that converges in the unit disk of
the complex field:

   f[x_] = Sum[ x^(n-1)/(n^3+n), {n, 1, Infinity} ]

With immediate assignment, f[x] is evaluated to a special function.
Suppose now that I need the derivative of f[x]. If I do it with

   D[ f[x], x ]

there is no problem: I get a regular-looking special function
combination. But if I try to get the derivative with


the output is a formula containing DirectedInfinity. Moreover

   f'[x] // Simplify

gives Indeterminate.

By the way, the integral

   Integrate[ (1-Cos[y])/(E^y-x), {y, 0, Infinity} ]

is left as it is by Mathematica, although it is equal to the special
function f[x] above, at least for many values of x.

My version is 3.0.1 for PowerMacintosh.

                     Gianluca Gorni

 | Gianluca Gorni                  |
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