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Assigning finite values to divergent series

Reijden, Bas van der (2019) Assigning finite values to divergent series. Bachelor's Thesis, Mathematics.


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In order to assign a finite value to a divergent series in a useful and mathematically justified way, it turns out that we can ‘extend’ the notion of the convergence of an infinite series by introducing so-called summation methods. After we have explained the basic principles of summability theory (the mathematical subfield concerning summation methods and their interrelationships), we will focus on a particular type of summation methods: Cesaro summation. We will show various properties of Cesaro summation accompanied with examples in which we apply the methods for assigning finite values to divergent series. Thereafter, we will construct a full generalization of Cesaro summation which seems to be able to sum more ‘wildly’ divergent series. Furthermore, for the defining series of the Riemann zeta function, the generalized method corresponds with the analytic continuation of this function. In conclusion, we show that the assigned values are not completely picked out of thin air and we will see which insights summability theory can give us in (pure) mathematics as well as other sciences.

Item Type: Thesis (Bachelor's Thesis)
Supervisor nameSupervisor E mail
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 24 Jan 2019
Last Modified: 29 Jan 2019 13:34

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