Indefinite integrals involving the incomplete elliptic integral of the third kind. Issue 8 (2nd August 2016)

• Record Type: Journal Article
• Authors: Conway, John T.
• Is Part Of: Integral transforms and special functions. Volume 27:Issue 8(2016)
• Page Start: 667
• Page End: 682
• Publication Date: 2016-08-02
• Subjects: Euler–Lagrange -- differential equations -- elliptic integrals; 70H03 -- 34A30 -- 33E05; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2016.1184662
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: A substantial number of new indefinite integrals involving the incomplete elliptic integral of the third kind are presented, together with a few integrals for the other two kinds of incomplete elliptic integral. These have been derived using a Lagrangian method which is based on the differential equations which these functions satisfy. Techniques for obtaining new integrals are discussed, together with transformations of the governing differential equations. Integrals involving products combining elliptic integrals of different kinds are also presented.