[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
terms:

        sum(1/(1+n^2),n,1,10000)

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

To calculate with floats, use

        sum(1/(1+float(n)^2),n,1,10000);
or
        sum(1.0/(1+n^2),n,1,10000);

                   => 1.076574052468745

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

        sum(1.0/(1+(10001-n)^2),n,1,10000)
                 => 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.

             -s


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