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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 HorvÃ¡t 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 HorvÃ¡t
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