#SUMMATION IN MATHEMATICA HOW TO#

Where is the Laurent series expansion of f about infinity. (a) If f has a pole of order at infinity, then Let’s define the general limit of f(z) as z approaches infinity, denoted by. Suppose the function f has a singularity at infinity. In Section 3 we give a table with comparison to the five most famous summation methods (Abel, Borel, Cesaro, Dirichlet and Euler) which are also used to find the sums of series from Section 2 and show that our method is the strongest (see for the history of the theory of summable divergent series). In Section 2 these sums are solved using Mathematica and general method for summing divergent series. In this section, we summarize without proofs the relevant results on the general method for summing divergent series and give the sums of some divergent series from Hardy’s book and Ramanujan’s notebook. As for prerequisites, the reader is expected to be familiar with real and complex analysis in one variable.

#SUMMATION IN MATHEMATICA HOW TO#

The aim of this paper is to show readers how to sum divergent series using the summation method discovered in our previous work and symbolic mathematical computation program Mathematica and make a comparison to other five summation methods implemented in Mathematica. We make a comparison to other five summation methods implemented in Mathematica and show that our method is the stronger method than methods of Abel, Borel, Cesaro, Dirichlet and Euler.

We are interested in finding sums of some divergent series using the general method for summing divergent series discovered in our previous work and symbolic mathematical computation program Mathematica.

Summation in mathematica