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MathGroup Archive 2007

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Re: Same Limit: OK in 5.2, fails in 6.0; Packages gone in 6.0 ???

  • To: mathgroup at smc.vnet.net
  • Subject: [mg78009] Re: Same Limit: OK in 5.2, fails in 6.0; Packages gone in 6.0 ???
  • From: "Rolf.Mertig at gmail.com" <Rolf.Mertig at gmail.com>
  • Date: Thu, 21 Jun 2007 05:45:28 -0400 (EDT)
  • References: <f5atqa$b75$1@smc.vnet.net>

Hi,
yes, there is a problem with Limit recognizing $Assumptions.
Find below a workaround.
Regards,

Rolf Mertig
http://www.gluonvision.com

Mathematica 6.0 for Linux x86 (32-bit)
Copyright 1988-2007 Wolfram Research, Inc.

In[1]:= !!limit
$Assumptions={a > 0, k1 > 0, k2 >0,Element[x,Reals]};
SetOptions[Limit, Assumptions -> $Assumptions];
i1b=1/a Integrate[Exp[-I k2 x] Exp[I k1 x],{x,-a/2,a/2}]
Limit[i1b, a -> Infinity]

In[1]:= <<limit

Out[1]= 0


On Jun 20, 11:59 am, jrc <jrch... at mcn.net> wrote:
> Why?
>
> I have,
>
> $Assumptions = {a > 0, k1 > 0, k2 >0, x e(in) Reals}
> (repeats ok)
>
> i1b = (1/a)* Integral from -a/2 to +a/2 of integrand:
>
>               exp(- i k2 x) exp(i k1 x) dx
>
> with the expected result,
>
> i1b = fraction with numerator = 2 Sin[(1/2)a(k1-k2)]
>                  and denominator = a(k1-k2)
>
> Now I want the limit of this result, as the parameter a goes to infinity:
>
> Limit[i1b, a -> Infinity]
>
> Mathematica 5.2 gives correct result, zero;
>    (note this is just lim(sin(x)/x, x -> inf), which is obviously zero)
>
> Mathematica 6.0 is unable to evaluate the limit.
>
> Ruskeepaa's "Navigator", 2nd ed, (written for v5.2) claims there
> is a package, "Calculus`Limit`" that makes 'Limit' work better
> (p. 395 and p. 430). However, no such package seems to exist in
> v6.0.
>
> How many packages no longer exist in 6.0 ???? Is there a list ????
>


> Can anyone give me a reason for this obvious failure?
>
> jrc






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