Antonio Jimenez Pastor, Veronika Elisabeth Pillwein,
"Differentially definable functions: a survey"
, in Gesellschaft für Angewandte Mathematik und Mechanik (GAMM): Proceedings in Applied Mathematics and Mechanics (PAMM), Vol. 21, Nummer 1, Seite(n) e202100178--e2021001, 2021
Differentially definable functions: a survey
Sprache des Titels:
Proceedings in Applied Mathematics and Mechanics (PAMM)
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)