#### Date of Award

Spring 5-8-2020

#### Level of Access Assigned by Author

Open-Access Thesis

#### Degree Name

Master of Arts (MA)

#### Department

Mathematics

#### Advisor

Julian Rosen

#### Second Committee Member

Jack Buttcane

#### Third Committee Member

Andrew Knightly

#### Abstract

Parseval's identity is an equality from Fourier analysis that relates an infinite series over the integers to an integral over an interval, which can be used to evaluate the exact value of some classes of infinite series. We compute the exact value of the Riemann zeta function at the positive even integers using the identity, and then we use it to compute the exact value of an infinite series whose summand is a rational function summable over the integers.

#### Recommended Citation

Poulin, James R., "Calculating Infinite Series Using Parseval's Identity" (2020). *Electronic Theses and Dissertations*. 3196.

https://digitalcommons.library.umaine.edu/etd/3196