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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: [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


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