The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math.symbolic

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: integral for fun
Replies: 25   Last Post: Mar 6, 2014 4:10 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Richard Fateman

Posts: 1,539
Registered: 12/7/04
Re: integral for fun
Posted: Mar 1, 2014 11:30 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 3/1/2014 5:28 AM, Jonas Matuzas wrote:
regarding integrals in terms of elementary functions (or well-known
constants ...)

>> RJF
> I agree with you. You can name my integral
> Matuzas[a]=Integrate[Cos[x]^4/(a^8 + x^8), {x, -\[Infinity],
> \[Infinity]}] as new function. But you have to do table of this
> integral properties: differentiation, integration, differential
> equation it supports, Fourier series, expressions with another
> functions.

It would still not be an elementary function, even if you had
all that information available.(Historical convention, I suppose.)

If you want to learn about
the search for a solution to the problem of (indefinite) integration
in terms of elementary functions, you can try to find work
by Liouville, and then a stream of work including Robert Risch,
but not ending there. Maybe Manuel Bronstein's work would be
most recent.

And everybody should use it :) How to evaluate numerical
> -it is no problem . Actually the same is with Ci, Si and ect...
> Numerically we know how to evaluate. But the same is with elementary
> functions, is'n it?

There is a question about how to do definite integrals. Maxima
obviously used a residue method rather than substitution into
the indefinite integral. Making a wrong choice in method can
waste a lot of time.

Maxima's residue methods are described in a PhD thesis by Paul S H. Wang
at MIT.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.