Convolutions of Liouvillian sequences. (November 2020)

• Record Type: Journal Article
• Authors: Abramov, Sergei A.; Petkovšek, Marko; Zakrajšek, Helena
• Is Part Of: Journal of symbolic computation. Volume 101(2020)
• Page Start: 73
• Page End: 89
• Publication Date: 2020-11
• Subjects: 68W30 -- 33F10; (Rationally) d'Alembertian sequences -- (Rationally) Liouvillian sequences -- Convolution -- Closure properties; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.02.016
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: While Liouvillian sequences are closed under many operations, simple examples show that they are not closed under convolution, and the same goes for d'Alembertian sequences. Nevertheless, we show that d'Alembertian sequences are closed under convolution with rationally d'Alembertian sequences, and that Liouvillian sequences are closed under convolution with rationally Liouvillian sequences.