Author

Zachary Cole

Date of Award

2020

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Area of Concentration

Mathematics

Abstract

The torsional rigidity of a piecewise smoothly bounded domain Ω ⊂R3 is a geometric invariant first studied in the context of elastic bodies. Torsional rigidity is well studied for many geometric bodies and plays an important role in analysis. We establish a formula for the torsional rigidity of a rectangular prism in terms of hyperbolic trig functions, special values of the Riemann zeta function, and double infinite sums over the odd positive integers. We use this formula to establish an identity for two infinite sums involving hyperbolic trig functions and special values of the Riemann zeta function.

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