#### Title (All Applicants)

#### Project Advisor(s) (Students Only)

Dr. Tom Bengtson

#### Presentation Type (All Applicants)

Oral Presentation

#### Location

IV-A-3: Hanson 102

#### Disciplines (All Applicants)

Mathematics

#### Description, Abstract, or Artist's Statement

The Fourier Series has always been a great tool by turning the most complicated functions into a simple approximation by several sine and cosine terms. However, given the fact that its called an approximation arouses the question of how accurate is this approximation, especially with functions that have a corner at x values. In this project, we will show how the series that is the sum of the reciprocals of squares arises in the study of Fourier series. We will discuss the convergence and the rate of convergence of this series. This result arose during exploration on mathematical software Sage. We will indicate some direction for future research.

#### Augustana Digital Commons Citation

Ibrahim, Hussam. "On the Sum of the Reciprocals of Squares" (2015). *Celebration of Learning.*

https://digitalcommons.augustana.edu/celebrationoflearning/2015/presentations/2

On the Sum of the Reciprocals of Squares

IV-A-3: Hanson 102

The Fourier Series has always been a great tool by turning the most complicated functions into a simple approximation by several sine and cosine terms. However, given the fact that its called an approximation arouses the question of how accurate is this approximation, especially with functions that have a corner at x values. In this project, we will show how the series that is the sum of the reciprocals of squares arises in the study of Fourier series. We will discuss the convergence and the rate of convergence of this series. This result arose during exploration on mathematical software Sage. We will indicate some direction for future research.