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.
Recommended Citation
Cole, Zachary, "TORSIONAL RIGIDITY AND INFINITE SUMS" (2020). Theses & ETDs. 5917.
https://digitalcommons.ncf.edu/theses_etds/5917