Dear MAXIMA users,
allow me to trouble You about the following matter. I need to evaluate
such integrals as
integrate(x^3/(exp(x)-1),x,0,INF),
in this particular case the result should be %pi^4/15. MAXIMA returns:
...
GCL (GNU Common Lisp) Version(2.3.8) Pá kvì 4 09:07:47 CEST 2001
Licensed under GNU Library General Public License
Contains Enhancements by W. Schelter
Maxima 5.5 Pá kvì 4 09:07:44 CEST 2001 (with enhancements by W. Schelter).
Licensed under the GNU Public License (see file COPYING)
...
(C2) integrate(x^3/(exp(x)-1),x,0,INF);
x x 2 x 3 x
(D2) (limit 6 LI (%E ) - 6 x LI (%E ) + 3 x LI (%E ) + x LOG(1 - %E )
x -> INF 4 3 2
4 4
x %PI
- --) - ----
... 4 15
I would like to ask, in what way the functions LI[n](x) are defined? If I
try
(C3) LI[4](1);
I got
4
%PI
(D3) ----
90
but for another x-argument MAXIMA does not return any numerical value,
e.g.
(C4) LI[4](2);
(D4) LI (2)
4
Thanks in advance for any hints!
Faithfully,
Lukas Richterek
--
Department of Theoretical Physics | tel.:+420-68-5222451, ext. 372
Fac. Nat. Sciences, | fax :+420-68-5225737
Palacky University | e-mail: richter@risc.upol.cz
Svobody 26, Olomouc, CZ-771 46 |
C z e c h R e p u b l i c | /|||\
http://aix.upol.cz/~richter/index.html ( o|o )
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