Differentially definable functions: a survey

Antonio Jimenez Pastor; Veronika Pillwein

doi:10.1002/pamm.202100178

Differentially definable functions: a survey

Antonio Jimenez Pastor, Veronika Pillwein

Research Institute for Symbolic Computation

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

Abstract Most widely used special functions, such as orthogonal polynomials, Bessel functions, Airy functions, etc., are defined as solutions to differential equations with polynomial coefficients. This class of functions is referred to as D-finite functions. There are many symbolic algorithms (and implementations thereof) to operate with these objects exactly. Recently, we have extended this notion to a more general class that also allows for good symbolic handling: differentially definable functions. In this paper, we give an overview on what is currently known about this new class. Conference: Special Issue: 91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)

Original language	English
Title of host publication	Proceedings in Applied Mathematics and Mechanics (PAMM)
Editors	Gesellschaft für Angewandte Mathematik und Mechanik (GAMM)
Number of pages	4
Volume	21
DOIs	https://doi.org/10.1002/pamm.202100178
Publication status	Published - 2021

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

JKU Focus areas

Digital Transformation

Access to Document

10.1002/pamm.202100178

Cite this

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