2006/05/08 by R. A. Krajcik, Krajcik, R. A., K. D. McLenithan +1
Materials Science · Mathematics · #26B15 #33E05 #51M25 #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Liquid Crystal Research Advancements #Mathematics and Applications #math.GM #msc:26B15 #msc:33E05 #msc:51M25
paper · pdf · doi:10.48550/arxiv.math/0605216
53 pages, 3 figures
arxiv created 2006/05/08 · openalex publication_date 2006/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Integrals related to the surface area of arbitrary ellipsoids are derived, evaluated, and compared with each other and existing integrals found in the literature. We clarify the literature on the ellipsoid area problem, which dates back to Legendre's original 1811 work. We derive and evaluate several additional integrals involving or evaluating to elliptic integrals. These new integrals are natural extensions of those found in the literature and constitute useful additions to standard integrals compendia.