A generalized integration formula for indefinite integrals of special functions. Issue 8 (2nd August 2020)

• Record Type: Journal Article
• Authors: Conway, John T.
• Is Part Of: Integral transforms and special functions. Volume 31:Issue 8(2020)
• Page Start: 586
• Page End: 600
• Publication Date: 2020-08-02
• Subjects: Differential equations -- cylinder functions -- modified cylinder functions -- Whittaker functions; 34B30 -- 33C10 -- 33C15; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2020.1721485
• Languages: English
• ISSNs: 1065-2469

Abstract

Abstract : An integration formula for generating indefinite integrals which was presented in Conway JT [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015;26(10):812–824], which involves an arbitrary function h x, is generalized to include two arbitrary functions s x and h x . In the new formula the Lagrangian factor f x of the original formula is replaced by a new factor f ¯ x, which is derived from s x . The use of the new formula is illustrated by deriving a number of integrals for cylinder and Whittaker functions, with several integrals combining Whittaker functions with cylinder and modified cylinder functions. Some of these integrals are among the best known results for these functions, whereas others are believed to be new. A number of new integrals of Whittaker functions are also presented which came directly from the derivatives needed to apply the integration formula. All results presented have been checked using Mathematica.