ON THE SURFACE-AREA OF AN ELLIPSOID AND RELATED INTEGRALS OF ELLIPTIC INTEGRALS

[摘要] By considering the integral of an arbitrary field on the surface of an ellipsoid of revolution from two different perspectives, two different expressions are derived for it. One of them has a complete elliptic integral as its kernel, while the other kernel is just a radical (albeit containing one additional integration). As the expressions with the latter kernel are often more readily evaluated, a new class of integrals (and some integral relations), having a complete elliptic integral as their kernel, have been established. As the integral, defining the surface area of an arbitrary ellipsoid, can also be transformed to the previous form, its value can be established in terms of elliptic integrals.

[发布日期] 1994-06-20

[关键词] SURFACE AREA ELLIPSOID;INTEGRALS OF ELLIPTIC INTEGRALS;COMPLETE ELLIPTIC INTEGRAL TRANSFORM