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

*To*: mathgroup at smc.vnet.net*Subject*: [mg56167] Re: [mg56120] Trouble with Limit[I ... k]/k, k-> Infinity]*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Sun, 17 Apr 2005 03:07:21 -0400 (EDT)*References*: <200504160751.DAA24601@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Christian Mikkelsen wrote: > I am struggling to valuate an intermediate result in a long calculation > and I get stuck with terms like this one: > > Limit[Exp[I k A]/k, k -> Infinity, Assumptions -> {A != 0, A \[Element] > Reals}] > > In the actual expression, A are somewhat more complicated expressions but > I am willing to tell Mathematica by hand that they are real and > non-zero, however, it still doesn't work. I don't see that there is a > problem in mathematical terms so how can I convince Mathematica to > give me an answer? > > Actually, Mathematica 5.1 does not mind telling me the result of > > Limit[Exp[I k]/k, k -> Infinity] > > At the moment I am relying on a kludge relying on pattern-matching but I > am not very good at it so there might be a point to help me on. > Any input or help will be greatly appreciated. > > > Thanks, > > Christian It is slightly tricky for the Limit 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 Limit[Exp[I*k*t]/k, k->Infinity, Assumptions->t<0] you get zero. I guess this means you will need to split into cases in such situations. Daniel Lichtblau Wolfram Research

**References**:**Trouble with Limit[I ... k]/k, k-> Infinity]***From:*Christian Mikkelsen <s010132@student.dtu.dk>