A Fast Approach to Creative Telescoping

Abstract

In this note we reinvestigate the task of computing creative telescoping relations in differential-difference operator algebras. Our approach is based on an ansatz that explicitly includes the denominators of the delta parts. We contribute several ideas of how to make an implementation of this approach reasonably fast and provide such an implementation. A selection of examples shows that it can be superior to existing methods by a large factor.

9 pages, 1 table, final version as it appeared in the journal

References in corpus (2)

• A Non-Holonomic Systems Approach to Special Function Identities
• A Proof of George Andrews' and Dave Robbins' q-TSPP Conjecture (modulo a finite amount of routine calculations)

Cited by in corpus (40)

• Iterated Binomial Sums and their Associated Iterated Integrals
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• Computing periods of rational integrals
• Creative Telescoping for Holonomic Functions
• Multiple binomial sums
• Irreducibility of q-difference operators and the knot 7_4
• Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices
• Explicit formula for the generating series of diagonal 3D rook paths
• Computing Periods of Hypersurfaces
• Phase Transition of Random Non-Uniform Hypergraphs
• $\epsilon$-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
• Permutations sortable by two stacks in parallel and quarter plane walks
• Diagonals of rational functions and selected differential Galois groups
• Constructing minimal telescopers for rational functions in three discrete variables
• A Generalized Apagodu-Zeilberger Algorithm
• Computing the volume of compact semi-algebraic sets
• Lattice Green Functions: the seven-dimensional face-centred cubic lattice
• Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
• Lattice Green Functions: the d-dimensional face-centred cubic lattice, d=8, 9, 10, 11, 12
• A numerical transcendental method in algebraic geometry
• Telescopers for Rational and Algebraic Functions via Residues
• Third order integrability conditions for homogeneous potentials of degree -1
• The ${\mathrm{A}}_2$ Andrews-Gordon identities and cylindric partitions
• A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape
• Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II
• Integrable homogeneous potentials of degree $-1$ in the plane with small eigenvalues
• The product of the eigenvalues of a symmetric tensor
• Master Lovas-Andai and Equivalent Formulas Verifying the $\frac{8}{33}$ Two-Qubit Hilbert-Schmidt Separability Probability and Companion Rational-Valued Conjectures
• A general method for calculating lattice Green functions on the branch cut
• Asymptotic lattice path enumeration using diagonals
• Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
• Trading Order for Degree in Creative Telescoping
• The generating function of Kreweras walks with interacting boundaries is not algebraic
• Telescoping method and congruences for double sums
• Some Open Problems related to Creative Telescoping
• An Algorithmic Approach to the $q$-Summability Problem of Bivariate Rational Functions
• Lazy Hermite Reduction and Creative Telescoping for Algebraic Functions
• An Algorithm for Deciding the Summability of Bivariate Rational Functions
• Order-Degree Curves for Hypergeometric Creative Telescoping
• Zeilberger's Holonomic Ansatz for Pfaffians