Document Type
Thesis
Degree Name
Master of Science (MSc)
Department
Mathematics
Faculty/School
Faculty of Science
First Advisor
Dr. Chester Weatherby
Advisor Role
Supervisor
Second Advisor
Dr. Shengda Hu
Advisor Role
Supervisor
Abstract
In this thesis we discuss the various approaches that will be taken to evaluate and find a finite closed form for the sum $$\sum_{n \in \mathbb{Z}} \frac{1}{(n^3+Bn^2+Cn+D)^k}$$ where $B, C, D \in \mathbb{C}$ and $k$ is a positive integer. We begin this thesis by studying the cubic equations and discussing briefly various methods of finding their roots. Cardano's method (1545) for finding the roots of cubic polynomials is explored in detail as this method is used in later parts of the thesis to make calculations while evaluating the sums. Various tools and techniques from Fourier analysis are reviewed for these aid in computing the sums. To obtain finite closed forms for the sums $\sum_{n \in \mathbb{Z}} \frac{1}{(n^3+Bn^2+Cn+D)^k}$, we make use of different methods and approaches from combinatorics and identities involving well-known trigonometric functions.
Recommended Citation
Virk, Gagandeep K., "Computing closed forms for the convergent series $\displaystyle\sum_{n \in \mathbb{Z}}\frac{1}{(n^3+Bn^2+Cn+D)^k}$" (2016). Theses and Dissertations (Comprehensive). 1886.
https://scholars.wlu.ca/etd/1886
Convocation Year
2016
Convocation Season
Fall