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Re: Re: Limit[(x - Log[Cosh ]) SinIntegral , x -> Infinity]

• To: mathgroup at smc.vnet.net
• Subject: [mg86989] Re: [mg86947] Re: Limit[(x - Log[Cosh ]) SinIntegral , x -> Infinity]
• From: "Szabolcs HorvÃt" <szhorvat at gmail.com>
• Date: Fri, 28 Mar 2008 03:16:00 -0500 (EST)
• References: <20080326082007.401$ci@newsreader.com>

On Thu, Mar 27, 2008 at 3:04 PM, Daniel Lichtblau <danl at wolfram.com> wrote:
> Szabolcs Horvát wrote:
>  > On Wed, Mar 26, 2008 at 1:20 PM, David W. Cantrell
>  >
>  > Actually a ClearSystemCache[] is enough, but since cached results can
>  > affect the success of calculations, probably it would be better if
>  > Mathematica did not cache the "result" that it *cannot* calculate
>  > something.
>  > [...]
>
>  I beg to differ. If that nonevaluation result is time consuming to
>  compute, and is something that might show up in a context where
>  recomputation is an issue, then caching can save considerable time.
>
>  Limits tend to be recomputed when one does, say, a definite integral
>  requiring several different tactics. Caching them thus can reduce
>  timings of Integrate, a notoriously slow function.

That is a very good point.

But I am still curious about why Mathematica can compute the two
limits separately but not the limit of their product.  I could imagine
that Limit[] has some built-in constraints, e.g. it only tries a
limited number of transformations on the expression, or it has some
internal time constraints.   If I understood correctly, Bob Hanlon
reported that Mathematica does give an answer on his computer---this
could be explained by time constraints and a faster computer.

If this is really the case, is there a way to ask Mathematica to work
"harder" (perhaps try longer), so that it will be able to give an
answer?  (For example, Simplify has the option TimeConstraint.)

Szabolcs Horvát