A computable extension for D-finite functions: DD-finite functions. (September 2019)

• Record Type: Journal Article
• Authors: Jiménez-Pastor, Antonio; Pillwein, Veronika
• Is Part Of: Journal of symbolic computation. Volume 94(2019)
• Page Start: 90
• Page End: 104
• Publication Date: 2019-09
• Subjects: Holonomic functions -- Closure properties -- Formal power series; 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.2018.07.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties.