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MathGroup Archive 2005

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg56159] Re: Trouble with Limit[I ... k]/k, k-> Infinity]
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Sun, 17 Apr 2005 03:07:04 -0400 (EDT)
  • References: <d3qgs6$oao$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Christian Mikkelsen <s010132 at student.dtu.dk> 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.

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

David


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