On the surface area of an ellipsoid and related integrals of elliptic integrals
type: Item
instance of: scholarly article
title: On the surface area of an ellipsoid and related integrals of elliptic integrals
zbMATH Open document ID: 0804.33017
DOI: 10.1016/0377-0427(92)00009-X
author: Leo R. M. Maas
published in: Journal of Computational and Applied Mathematics
publication date: 1994-09-26T00:00:00Z
review text: The paper deals with integrals of an arbitrary field \(F(x,y,z)\) on the surface area of an ellipsoid \[ S:= \biggl\{ (x,y,z)\in \mathbb{R}^ 3 \mid {{x^ 2} \over {a^ 2}} + {{y^ 2} \over {b^ 2}} + {{z^ 2} \over {c^ 2}} =1 \biggr\}. \] Different orientations of the coordinate axes lead to different (equivalent) integral expressions. Specific choices of the field \(F(x,y,z)\) enable the author to evaluate (or to derive various identities among) integrals containing complete elliptic integrals (of the second kind) as their kernels. As an application the surface area of an arbitrary ellipsoid can be obtained explicitly.
Mathematics Subject Classification ID: 33E05
Mathematics Subject Classification ID: 44A20
zbMATH DE Number: 644310
zbMATH Keywords: surface area of ellipsoid
zbMATH Keywords: complete elliptic integrals
reviewed by: J. Saurer
MaRDI profile type: Publication
cites work: Q5577281
cites work: Q4175520
cites work: Q3663962
cites work: Q4002460
description: scientific article; zbMATH DE number 644310