Date of Graduation

Spring 2017

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Shelby Kilmer

Keywords

analytic function, homotopy, singularity, pole, zero, residue, Bernoulli numbers, finite sums, infinite series

Subject Categories

Mathematics

Abstract

A large number of infinite sums, such as , cannot be found by the methods of real analysis. However, many of them can be evaluated using the theory of residues. In this thesis we characterize several methods of summations using residues, including methods integrating residues and the Bernoulli numbers. In fact, with this technique we derive some summation formulas for particular Finite Sums and Infinite Series that are difficult or impossible to solve by the methods of real analysis.

Copyright

© Mohammed Saif Alotaibi

Open Access

Included in

Mathematics Commons

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