Definitions of LI[n](x) functions



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    | 
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http://aix.upol.cz/~richter/index.html   ( o|o ) 
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