Tee, Garry J.2009-08-282009-08-282004-03Department of Mathematics - Research Reports-513 (2004)1173-0889http://hdl.handle.net/2292/5112The surface area of a general $ n $-dimensional ellipsoid is represented as an Abelian integral, which can readily be evaluated numerically. If there are only 2 values for the semi-axes then the area is expressed as an elliptic integral, which reduces in most cases to elementary functions. The capacity of a general $ n $-dimensional ellipsoid is represented as a hyperelliptic integral, which can readily be evaluated numerically. If no more than 2 lengths of semi-axes occur with odd multiplicity, then the capacity is expressed in terms of elementary functions. If only 3 or 4 lengths of semi-axes occur with odd multiplicity, then the capacity is expressed as an elliptic integral.https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htmTechnical ReportFields of Research::230000 Mathematical Sciences::230100 MathematicsThe author(s)