clicliclic at (no spam) freenet.de wrote:
What percentage of the *definite* integrals in the Gradshteyn-Ryzhik
collection still cannot be found by simply typing them into the latest
computer algebra systems?

The more people document their experience the more accurate the
estimate will be!


If you type them all into a Maple sheet (say in arrays) others
would try some ... or not It would be quite boring.

What percentage of the *definite* integrals in the Gradshteyn-Ryzhik
collection still cannot be found by simply typing them into the latest
computer algebra systems?

The problem with that is that some CAS have tables of integrals built-in,
and, theoretically speaking, putting enough labor into it, could include all
Gradshtein-Ryzhik integrals in these tables. That doesn't say much about
their actual possibilities.

What percentage of the *definite* integrals in the Gradshteyn-Ryzhik
collection still cannot be found by simply typing them into the latest
computer algebra systems?

The more people document their experience the more accurate the
estimate will be!

Martin.

What percentage of the *definite* integrals in the Gradshteyn-Ryzhik
collection still cannot be found by simply typing them into the latest
computer algebra systems?

But all this doesn't affect the answerability, or practical relevance
(assuming that Gradshteyn-Ryzhik covers what is of interest to a
user), of the original question.

If I wanted to know that for some meaningful purpose, I would, probably, use
a statistical approach - take a randomly chosen sample, say 100 integrals,
and try them.

Alec

But all this doesn't affect the answerability, or practical relevance
(assuming that Gradshteyn-Ryzhik covers what is of interest to a
user), of the original question.

Alec Mihailovs schrieb:
What percentage of the *definite* integrals in the Gradshteyn-Ryzhik
collection still cannot be found by simply typing them into the
latest computer algebra systems?

The problem with that is that some CAS have tables of integrals
built-in, and, theoretically speaking, putting enough labor into it,
could include all Gradshtein-Ryzhik integrals in these tables. That
doesn't say much about their actual possibilities.

Yes, the score of a particular candidate system might well be a
measure of its creators' stamina rather than their mathematical
ingenuity. Indeed, the electronic version of Gradshteyn-Rytzhyk would
in all likelihood score above 99%. And even this candidate could
perhaps be justly marketed as involving "sophisticated pattern-
matching algorithms". :-)

But all this doesn't affect the answerability, or practical relevance
(assuming that Gradshteyn-Ryzhik covers what is of interest to a
user), of the original question.

If we had a superb CAS, then the suggested programme would uncover errors,
if any, in the Gradshtein-Ryzhik integrals.

In article <20080619111752.654$xm at (no spam) newsreader.com>, David W. Cantrell
DWCantrell at (no spam) sigmaxi.net> wrote:

If we had a superb CAS, then the suggested programme would uncover errors,
if any, in the Gradshtein-Ryzhik integrals.

I recall back in 1980 or so, when the integration routines in MACSYMA
were written, they tried them out on standard integral tables, and
found many errors in those tables. I forget the figure, maybe 20
percent?

What percentage of the *definite* integrals in the Gradshteyn-Ryzhik
collection still cannot be found by simply typing them into the latest
computer algebra systems?

The more people document their experience the more accurate the
estimate will be!

Martin.

Most probably, Wolfram Research folks know a good approximation to
crack tangibly your tough nut. :)

At least one of them might be at vacation now ))

Anyways, our calculations show that the integrals involving at least
1 parameter present a challenge for the modern computer algebra
systems.