New method for summing divergent series

06/12/2015 - 21:21 von sinisa.bubonja | Report spam
Abstract. 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. 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.

https://m4t3m4t1k4.wordpress.com/20...n-methods/
 

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#1 Gottfried Helms
07/12/2015 - 03:18 | Warnen spam
Am 06.12.2015 um 21:21 schrieb :
Abstract. 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. 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.

https://m4t3m4t1k4.wordpress.com/20...n-methods/



I've not read through your full article, but you *should* explain (in your text)
why sum (6) and sum(8) do not differ by 1.

(6) : 1 +2 +3 +4 +5 +... = -1/12 ( zeta(-1) - known by zeta-regularization)
(8) : 2 +3 +4 +5 +6 +... = -7/12 ( why zeta(-1)+zeta(0) and not zeta(-1)-1 ?)

The reason is the type of summation method and the final
sum should always indicate, by what limit the series was

found (is it sum_{k=2}^\infty (k)
or is it sum_{k=1}^\infty (k) + \sum_{k=1}^\infty (1) )

Otherwise such a collection of formulae (and then also the
mathematical software) is very likely misleading.

Gottfried

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