A third integrating factor for indefinite integrals of special functions. Issue 12 (1st December 2020)

• Record Type: Journal Article
• Authors: Conway, John T.
• Is Part Of: Integral transforms and special functions. Volume 31:Issue 12(2020)
• Page Start: 941
• Page End: 954
• Publication Date: 2020-12-01
• Subjects: Differential equations -- cylinder functions -- parabolic cylinder functions -- Whittaker functions; 34B30 -- 33C05 -- 33C15; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2020.1777115
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: An integrating factor f ~ x is presented involving the terms in y ′ ′ x and q x y x of the general homogenous second-order linear ordinary differential equation. The new integrating factors obey second-order differential equations, rather than being given by quadrature. The new factors provides old and new integrals for special functions which obey such differential equations. The functions considered here are cylinder functions, parabolic cylinder functions and Whittaker functions. All the integrals given have been checked using Mathematica.