Mathematica Stack Exchange is a question and answer site for users of Mathematica. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I defined a function as:

g[b_] := Integrate[f[n]Exp[-b  DA (n.u)^2], n]


 D[g[b], b] /. b -> 0


(-DA)*Integrate[(n.u)^2*f[n], n]

But, then, how can

Series[g[b], {b, 0, 2}]


Integrate[f[n], n]

I guess there is something basic I don't understand. Something with order of evaluation? It's like b = 0 is evaluated before the differentiation in Series.

share|improve this question
Please give reason for negative votes so I can learn! – Sune Nov 3 '13 at 7:34
I guess formatting (please read these guidelines). Also,your code is not self-contained. There are undefined symbols, like f, u and DA. – Sjoerd C. de Vries Nov 3 '13 at 7:59
What do you think that n.u means? You use n as the integration variable, so it is one-dimensional. N.u is a vector operation. – Sjoerd C. de Vries Nov 3 '13 at 8:05
a dot product of n and u – Sune Nov 3 '13 at 8:06
And thanks for feedback about the post formatting etc. f u and Da are supposed to not be defined, because they are undefined to Mathematica. – Sune Nov 3 '13 at 8:08

Not answer, but an observation of where the problem is (too small to fit in comment).

If you simplify the function to

  g[b_] := Integrate[ f[n] Exp[-b n ], n];

Now, applying Series[g[x],{x,0,1}], and applying the Series manually (from definition) to see the difference:

  (g[b] /. b -> 0) + (D[g[b], b] /. b -> 0) x

Mathematica graphics

Now using the Series command:

  Series[g[x], {x, 0, 1}]

Mathematica graphics

Ok, so where is the problem? Series is not integrating it correctly when there is a b inside Exp[] (b is the input symbol to the function). This works:

   g[b_] := Integrate[ f[n] Exp[-n], n];

But once b is added inside the integrand and has to be inside Exp[], it fails. Need more Tracing to find where exactly it failed.

Note: I think this is a bug. I verified with Maple, and it gives the results, which matches the manual method:

Mathematica graphics

share|improve this answer
Agree so far :-) – Sune Nov 3 '13 at 9:12
I also feel this is a bug. Note, BTW, that the O[x]^3 is suspiciously missing. – Sjoerd C. de Vries Nov 3 '13 at 9:52
The missing O[x]^3 is also consistent with x=0 being (inapproriately) evaluated before the differentiation... – Sune Nov 3 '13 at 9:57
@sune I don't think so. It's even there (unnecessary) in Series[x, {x, 0, 2}]. – Sjoerd C. de Vries Nov 3 '13 at 10:10
Workaround: Block[{g}, Series[g[b], {b, 0, 2}]]. – Michael E2 Nov 3 '13 at 14:58

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.