D vs. Derivative
- To: mathgroup at smc.vnet.net
- Subject: [mg15601] D vs. Derivative
- From: Gianluca Gorni <gorni at dimi.uniud.it>
- Date: Thu, 28 Jan 1999 04:23:30 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello!
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
f'[x]
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
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| Gianluca Gorni |
| Universita` di Udine |
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