Trouble with Limit[I ... k]/k, k-> Infinity]

*To*: mathgroup at smc.vnet.net*Subject*: [mg56170] Trouble with Limit[I ... k]/k, k-> Infinity]*From*: Christian Mikkelsen <s010132 at student.dtu.dk>*Date*: Sun, 17 Apr 2005 03:07:28 -0400 (EDT)*Organization*: UNI-C*Sender*: owner-wri-mathgroup at wolfram.com

Thank you all for the various answers and suggestions (sent directly to me or otherwise). Let me summarize. yehuda: > May be it will be a good idea to break the original expression into > these two subexpressions? The original expression is very large (LeafCount[] ~40000) and contains many slightly different instances of Limit[Exp[I A k]/k, k-> Infinity] among other things. The less I have to do by hand the better. David: > My suggestion is to use ComplexExpand prior to asking for the limit. (I > also dropped the condition that A be nonzero since it seemed > irrelevant.) > > In[3]:= > Assuming[Element[A, Reals], > Limit[ComplexExpand[Exp[I*A*k]]/k, k -> Infinity]] > > Out[3]= > 0 This seems to be the best bet. I agree that it is silly to write {a != 0}. I wonder why it works. Peter Pein: > Union[Limit[ > Exp[I k A]/k, k -> Infinity, Assumptions -> #] & /@ {A > 0, A < 0}] Clever, I didn't realize that this was a way. Daniel: > I think it is slightly tricky for the internal code to figure out that > there are two possibilities that behave in the same way. If you do > > Limit[Exp[I*k*t]/k, k->Infinity, Assumptions->t>0] > > or > you get zero. I guess this means you will need to split into cases in > such situations. The trouble is that this is not a question of two cases in my actual example. I am still struggling to understand the structure of the resulting expression. I realize that it can be hard for Mathematica for find its way around some expressions but I am happy to help :-) The trouble is sometimes how. In my case, I pattern match to replace Exp[I _ k_|-I _ k_]/_ k_^n_ by k^n and (by the way) ExpIntegral[I (...) k] by I Pi Sign[(...)] as (...) is real. This seems ugly but, I hope, right in my cases. Chris: > For example: I had some expressions describing a three (ideal) gas > mixture. Mathematica could not integrate them until I had told it the > domain of every variable in the integration *and* that the sum of > every combination of two mol fractions was less than 1. In my case, I go on to evaluate the result by integration and this I have not made work yet. Unfortunately, I will have to take care of a great number of cases. Thanks a lot of the help. I will post a follow up to ask for more help. Christian