Michael Somos on Fri, 29 Oct 1999 16:39:11 -0400 (EDT)

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dilog() bug

                    GP/PARI CALCULATOR Version 2.0.17 (beta)
                i686 running linux (ix86 kernel) 32-bit version
              (readline v2.2 enabled, extended help not available)

                           Copyright (C) 1989-1999 by
          C. Batut, K. Belabas, D. Bernardi, H. Cohen and M. Olivier.

Type ? for help, \q to quit.
Type ?12 for how to get moral (and possibly technical) support.

   realprecision = 28 significant digits
   seriesprecision = 16 significant terms
   format = g0.28

parisize = 4000000, primelimit = 500000
gp> polylog(2,10)
%1 = 0.5363012873578627365501597698 - 7.233784412415464812490046550*I
gp> dilog(10) 
%2 = 0.5363012873578627365501597699 - 7.233784412415464812490046550*I
gp> \ps3
   seriesprecision = 3 significant terms
gp> polylog(2,x)
%3 = x + 1/4*x^2 + O(x^3)
gp> dilog(x)
  ***   incorrect type in comparison.

It seems to me that polylog(2,x) and dilog(x) shuould give essentially
the same answer for any value of x. In fact, I would define it as follows:


Any reason why this is not the case? Shalom, Michael

Michael Somos <somos@grail.cba.csuohio.edu>     Cleveland State University
http://grail.cba.csuohio.edu/~somos/            Cleveland, Ohio, USA 44115