Applications of Caputo operators in the evaluation of Clebsch–Gordan-type multiple elliptic integrals. Issue 5 (4th May 2023)

• Record Type: Journal Article
• Authors: Campbell, J. M.
• Is Part Of: Integral transforms and special functions. Volume 34:Issue 5(2023)
• Page Start: 371
• Page End: 383
• Publication Date: 2023-05-04
• Subjects: Integral transform -- fractional operator -- complete elliptic integral -- Clebsch–Gordan integral; 33C75 -- 26A33 -- 33E05; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2022.2128798
• Languages: English
• ISSNs: 1065-2469

Abstract

Abstract : We apply a method of semi-integration by parts (SIBP) that we had previously derived and formulated using the semi-derivative and semi-primitive operators. We obtain many new results on integrals involving the complete elliptic integrals as integrand factors, building on the work of Glasser, Cantarini, Wan, and Zhou. Our main results have not appeared in past literature concerning integrals involving products of the complete elliptic integral(s) of the first and/or second kinds. Furthermore, many previously known identities for such integrals are special cases of our SIBP identity for analytic functions.