Journal ArticleDOI
Integration of solutions of linear functional equations
Sergei A. Abramov,Mark van Hoeij +1 more
Reads0
Chats0
TLDR
The notion of the adjoint Ore ring was introduced in this paper, and a definition of an adjoint polynomial, operator and equation was given for integrating solutions of Ore equations.Abstract:
We introduce the notion of the adjoint Ore ring and give a definition of an adjoint polynomial, operator and equation. We apply this for integrating solutions of Ore equations. ∗read more
Citations
More filters
Journal ArticleDOI
A new Sigma approach to multi-summation
TL;DR: A general algorithmic framework that allows not only to deal with summation problems over summands being rational expressions in indefinite nested sums and products, but also over @?-finite and holonomic summand expressions that are given by a linear recurrence is presented.
Journal ArticleDOI
Univariate ore polynomial rings in computer algebra
TL;DR: A computer algebra library for basic operations in an arbitrary Ore ring can be used as a basis for various algorithms in Ore rings, in particular, in differential, shift, and q-shift rings.
Posted Content
Ore Polynomials in Sage
TL;DR: Sage as discussed by the authors is a Sage implementation of Ore algebras, which includes basic arithmetic and actions; gcrd and lclm; D-finite closure properties; natural transformations between related algebraes; guessing; desingularization; solvers for polynomials, rational functions and (generalized) power series.
Book ChapterDOI
Ore Polynomials in Sage
TL;DR: A Sage implementation of Ore algebras with main features for the most common instances include basic arithmetic and actions, GCRD and LCLM, and solvers for polynomials, rational functions and (generalized) power series.
Journal Article
Explicit formula for the generating series of diagonal 3D rook paths
TL;DR: The computer-driven discovery and proof of the fact that the generating series G(x) =sum n \geq 0 a_n x^n admits the following explicit expression in terms of a Gaussian hypergeometric function is described.
References
More filters
Journal ArticleDOI
Decision procedure for indefinite hypergeometric summation
TL;DR: In this paper, a sum-mand an is given and the goal is to find those S(n) with the property [Formula: see text] with respect to a given an.
Journal ArticleDOI
An extension of Zeilberger's fast algorithm to general holonomic functions
TL;DR: Zeilberger's fast algorithm for definite hypergeometric summation to non-hypergeometric holonomic sequences is extended and generalizes to the differential case and to q-calculus as well.
Journal ArticleDOI
Rational solutions of linear differential and difference equations with polynomial coefficients
TL;DR: Linear differential and difference equations whose coefficients and right-hand sides are polynomials are considered in this article, where the problem of constructing all rational solutions of an equation is solved.