D-Finiteness: A Success Story

A considerable portion of the work on special functions in computer algebra during the past decades was focused on D-finite functions. This focus was chosen for good reasons, as the concept of D-finiteness has proven to provide a fairly good compromise between, on the one hand, covering as many functions as possible, and on the other hand, keeping the class of functions restricted enough that computations stay reasonably efficient. In the talk, we will illustrate how questions about D-finite functions naturally arise in applications and how computer algebra is nowadays routinely used to answer such questions.

• Publication year

  2025

• Venue

  International Symposium on Symbolic and Algebraic Computation

• Publication date

  2025-07-28

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1145/3747199.3770904
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Bounds for D-Algebraic Closure Properties

  2025cited by this paper
• Positivity Proofs for Linear Recurrences with Several Dominant Eigenvalues

  2025cited by this paper
• Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach

  2024cited by this paper
• Hardinian Arrays

  2024cited by this paper
• D-Algebraic Functions

  2023cited by this paper
• Some D-finite and some Possibly D-finite Sequences in the OEIS

  2023cited by this paper
• D-Finite Functions

  2023cited by this paper
• Validated Numerics: Algorithms and Practical Applications in Aerospace

  2022cited by this paper
• The art of algorithmic guessing in gfun

  2022cited by this paper
• Combinatorics of permutations

  2022cited by this paper
• How does the Gerrymander Sequence Continue?

  2022cited by this paper
• Guessing with Little Data

  2022cited by this paper
• The gerrymander sequence, or A348456

  2022cited by this paper
• Binomial Determinants for Tiling Problems Yield to the Holonomic Ansatz

  2021cited by this paper
• Computer Algebra in the Service of Enumerative Combinatorics

  2021cited by this paper
• Congruences and telescopings of P-recursive sequences

  2021cited by this paper
• A hypergeometric proof that Iso is bijective

  2021cited by this paper
• Walsh functions, scrambled $(0, m, s)$-nets, and negative covariance: applying symbolic computation to quasi-Monte Carlo integration

  2020cited by this paper
• On the Uniqueness of Clifford Torus with Prescribed Isoperimetric Ratio

  2020cited by this paper
• Stieltjes moment sequences for pattern-avoiding permutations

  2020cited by this paper
• Periodic Pólya Urns and an Application to Young Tableaux

  2018cited by this paper
• Functions

  2018cited by this paper
• Supercongruences for polynomial analogs of the Apéry numbers

  2018cited by this paper
• Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences

  2017cited by this paper
• Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters

  2016cited by this paper
• Hypergeometric expressions for generating functions of walks with small steps in the quarter plane

  2016cited by this paper
• Series extension: predicting approximate series coefficients from a finite number of exact coefficients

  2016cited by this paper
• Graph Enumeration

  2016cited by this paper
• Lattice Path Enumeration

  2015influential reference
• Automated discovery and proof of congruence theorems for partial sums of combinatorial sequences

  2015cited by this paper
• Recent progress in an algebraic analysis approach to linear systems

  2014cited by this paper
• Bounds for D-finite closure properties

  2014cited by this paper
• A difference ring theory for symbolic summation

  2014cited by this paper
• Desingularization of Ore operators

  2014cited by this paper
• A Diffie-Hellman-like Key Exchange Protocol Based on Multivariate Ore Polynomials

  2014cited by this paper
• The ABC of Creative Telescoping - Algorithms, Bounds, Complexity

  2014cited by this paper
• Creative Telescoping for Holonomic Functions

  2013cited by this paper
• Computer Algebra in Quantum Field Theory

  2013cited by this paper
• Complexity estimates for two uncoupling algorithms

  2013cited by this paper
• Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

  2013cited by this paper
• Sparsity optimized high order finite element functions for H(curl) on tetrahedra

  2013cited by this paper
• Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

  2012cited by this paper
• Galois Theory of Linear Differential Equations

  2012cited by this paper
• Irreducibility of q-difference operators and the knot 7_4

  2012cited by this paper
• Sparsity optimized high order finite element functions for H(div) on simplices

  2012cited by this paper
• Fast computation of common left multiples of linear ordinary differential operators

  2011cited by this paper
• The Noncommutative A-Polynomial of (−2, 3, n) Pretzel Knots

  2011cited by this paper
• Holonomic gradient descent and its application to the Fisher-Bingham integral

  2011cited by this paper
• Advanced applications of the holonomic systems approach

  2010cited by this paper
• A Proof of George Andrews' and David Robbins' $q$-TSPP Conjecture

  2010cited by this paper
• The dynamic dictionary of mathematical functions

  2010cited by this paper
• Proof of George Andrews’s and David Robbins’s q-TSPP conjecture

  2010cited by this paper
• Effective bounds for P-recursive sequences

  2009cited by this paper
• A Complete Invariant Generation Approach for P-solvable Loops

  2009cited by this paper
• Coding with skew polynomial rings

  2009cited by this paper
• High-order Fuchsian equations for the square lattice Ising model: χ(6)

  2009cited by this paper
• High order Fuchsian equations for the square lattice Ising model:

  2009cited by this paper
• Products of ordinary differential operators by evaluation and interpolation

  2008cited by this paper
• Computing the complexity for Schelling segregation models

  2008cited by this paper
• Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

  2008cited by this paper
• Walks with small steps in the quarter plane

  2008cited by this paper
• Experiments with a Positivity-Preserving Operator

  2007cited by this paper
• Extended rate, more GFUN

  2007cited by this paper
• The Holonomic Ansatz II. Automatic Discovery(!) And Proof(!!) of Holonomic Determinant Evaluations

  2007cited by this paper
• Skew-cyclic codes

  2006cited by this paper
• D-finiteness: algorithms and applications

  2005cited by this paper
• Apparent singularities of linear difference equations with polynomial coefficients

  2004cited by this paper
• On the Number of Benzenoid Hydrocarbons

  2002cited by this paper
• Fast Evaluation of Holonomic Functions Near and in Regular Singularities

  2001cited by this paper
• An extension of Zeilberger's fast algorithm to general holonomic functions

  2000cited by this paper
• Computing the Galois group of a polynomial using linear differential equations

  2000cited by this paper
• Desingularization of linear difference operators with polynomial coefficients

  1999cited by this paper
• Fast Evaluation of Holonomic Functions

  1999cited by this paper
• Non-Commutative Elimination in Ore Algebras Proves Multivariate Identities

  1998cited by this paper
• A holonomic systems approach to special functions identities

  1990cited by this paper
• A fast algorithm for proving terminating hypergeometric identities

  1990cited by this paper
• Symmetric functions and P-recursiveness

  1990cited by this paper
• The diagonal of a D-finite power series is D-finite

  1988cited by this paper
• Some Congruences for the Apery Numbers

  1985cited by this paper
• Resurrecting the asymptotics of linear recurrences

  1985cited by this paper
• Differentiably Finite Power Series

  1980cited by this paper

• No citing papers are available for this paper.