Re: Another Out of Memory Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg91314] Re: Another Out of Memory Problem
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 15 Aug 2008 06:53:06 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g8137j\$19\$1@smc.vnet.net>

Kevin J. McCann wrote:

> I can do the following:
>
> Integrate[Cos[2*x]*
>       Exp[I*z*Cos[x]],
>     {x, -Pi, Pi}]
>
>
> which produces a Bessel function answer; however if I change the
> argument in the cosine to 2.5 as in:
>
> Integrate[Cos[2.5*x]*
>       Exp[I*z*Cos[x]],
>     {x, -Pi, Pi}]
>
> I almost immediately get this:
>
> No more memory available.
> Mathematica kernel has shut down.
> Try quitting other applications and then retry.
>
> Any ideas why? I am running XP with 2Gb of memory.

When using symbolic function (i.e. Integrate rather than NIntegrate,
Solve rather than NSolve, etc.) it is always a good idea to feed the
function with *exact* (infinite precision) numbers, thus 5/2 rather 2.5
in your case. (Mathematica does not find any closed form for your
integrand. Note that it take a while to compute but memory consumption
is under control.)

In[1]:= Integrate[Cos[5/2*x]*Exp[I*z*Cos[x]], {x, -Pi, Pi}]

Out[1]=

I z Cos[x]     5 x
Integrate[E           Cos[---], {x, -Pi, Pi}]
2

Regards,
-- Jean-Marc

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