A univariate function is called D-finite if it satisfies a linear differential equation with
polynomial coefficients. The concept of D-finiteness applies more generally to sequences …

We review our algebraic framework for linear boundary problems (concentrating on ordinary
differential equations). Its starting point is an appropriate algebraization of the domain of …

Creative telescoping is the method of choice for obtaining information about definite sums or
integrals. It has been intensively studied since the early 1990s, and can now be considered …

We prove that the algebra of integro-differential operators on a polynomial algebra is a
prime, central, catenary, self-dual, non-Noetherian algebra of classical Krull dimension n …

This thesis treats normal forms of matrices over rings of Ore polynomials. The whole thesis is
divided in three parts: First, Ore polynomials are described and basic facts about them are …

We develop an efficient algorithm for computing polynomial solutions of linear integro-
differential equations. Considering a linear integro-differential operator written in normal …

In this paper, we study the consequences of the fundamental theorem of calculus from an
algebraic point of view. For functions with singularities, this leads to a generalized notion of …

We propose a general algorithmic approach to noncommutative operator algebras
generated by additive operators using quotients of tensor rings that are defined by tensor …

Artstein's results show that a first-order linear differential system with delayed inputs is
equivalent to a first-order linear differential system without delay under an invertible …

Introduction. We present a Maple package for computing in algebras of integro-differential
operators. This provides the appropriate algebraic setting for treating boundary problems [7] …