levin_u_transform

Hi,

Here is a rough implementation of the Levin u-transform in maxima.
http://www.bertold.org/levin/

Example

load("levin.mac");
levin_u_sum(1/n^2,n,1,10);   /* we use 10 terms */

 3899836039
----------------
2370816000

float(%);

        1.644934081345832

fpprec:50;                         /* desired precision is 50 digits,
internal computations use 56 digits */
bflevin_u_sum(1/n^2,n,1);
         1.6449340668482264364724151666460251892189499012068b0
load("bffac");
bfzeta(2,50);
        1.6449340668482264364724151666460251892189499012068b0

I have one remaining problem. Whereas bflevin_u_sum(1/n^2,n,1) converges
very quickly
bflevin_u_sum(1/n^(201/100),n,1) does not converge at all. It would be
nice if somebody could explain this to me.

Regards,
Michel