Project Advisor(s)

Dr. Tom Bengtson

Presentation Type

Oral Presentation

Location

IV-A-3: Hanson 102

Disciplines

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.

Included in

Mathematics Commons

Share

COinS
 
May 6th, 2:15 PM May 6th, 3:15 PM

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.