Drexel dragonThe Math ForumDonate to 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.independent

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: 1,446
Registered: 12/7/04
Re: integral for fun
Posted: Mar 4, 2014 1:38 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 3/3/2014 7:24 AM, hebisch@math.uni.wroc.pl wrote:
> On Friday, February 28, 2014 11:33:56 PM UTC-5, Richard Fateman wrote:
>> I don't consider a solution that includes
>> Si, Ci, or hypergeometric functions as a solution
>> in closed form in terms of elementary functions.
>> Unless there is no way of expressing the answer in
>> terms of elementary functions.
>> After all, you could always decide that the
>> difficult integral in question deserves its own
>> name, say FooI, and then return the answer in terms
>> of FooI.

> _Indefinite_ integral above can not be done using elementary
> functions. For such integral 'li' and 'Ei' play the same
> as logarithms. 'Ci' and 'Si' are similar to 'atan'.
> As long as CAS can compute needed limits at infinity computing
> indefinite integral in terms of special functions
> is valid method of computing definite integral.
> And it is much more general than methods based on
> residue theorem.
> Waldek Hebisch

If your goal is not to compute a result in terms of elementary
functions but to allow terms of the "higher" or "special" functions
of applied mathematics, that's fine.

You just have to draw the
line somewhere, e.g. functions in Abramowitz and Stegun. or
the NIST digital library.

One of the uses of computer algebra systems is to find
explicit formulas when possible, and it is a puzzle whether
to use more functions, e.g. Si, Ci, Li; or just express
those and other functions as hypergeometric functions.
So the idea of what is needed for an explicit solution
is somewhat fluid. Macsyma for example, generally doesn't use
division internally. a/b is really a* (b^(-1)).
A trade-off between minimizing the number of different
functions and convenience. For display purposes, Macsyma
prints a/b. (free Maxima = Macsyma essentially)

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 1994-2016. All Rights Reserved.