Automatic reduction of elliptic integrals using Carlson's relations

In a series of papers, B. C. Carlson produced tables of elliptic integrals, evaluating them in terms of easily computed symmetrical functions, using a group of multivariate recurrence relations. These relations are, however, cumbersome to use by hand and, in the absence of a specific reductive algorithm, difficult to use with computer algebra. This paper presents such an algorithm, guaranteed to reduce a general elliptic integral to a set of fundamental ones.

• Type: Journal
• Year: 2002
• Where: MOC
• Authors: Norman Gray
• Keywords: Elliptic Integral, MOC 2002, Multivariate Recurrence Relations, Specific Reductive Algorithm