[Maxima] Numerical summation of series

Stavros Macrakis macrakis at alum.mit.edu
Sun Dec 24 08:22:10 CST 2006

I don't believe Maxima has any automatic way of summing infinite
series numerically.  It is easy enough to sum to a given number of


calculates the result in exact rationals, giving a huge but exact
result.  Floating that result gives 1.075674547634748.

To calculate with floats, use


                   => 1.076574052468745

This naively sums starting with n=1, so has a larger error (14 ulp) than say

                 => 1.076574052468748

which is exact.

> sum(1/(1+n^2),n,1,inf)
> numerically? Setting numer:true and applying float(-) did not seem to have
> any effect (except for replacing 1 by 1.0).
> The Levin u-transform is an often used method for summing such series

It would be great if you could contribute this method to Maxima.


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