Date of Graduation
Master of Science in Mathematics
analytic function, homotopy, singularity, pole, zero, residue, Bernoulli numbers, finite sums, infinite series
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.
© Mohammed Saif Alotaibi
Alotaibi, Mohammed Saif, "Residues, Bernoulli Numbers and Finding Sums" (2017). MSU Graduate Theses. 3172.