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Creative Telescoping for Holonomic Functions - MaRDI portal

Creative Telescoping for Holonomic Functions (Q5244921)

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scientific article; zbMATH DE number 6422048

Language	Label	Description	Also known as
English	Creative Telescoping for Holonomic Functions	scientific article; zbMATH DE number 6422048

Statements

scholarly article

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Creative Telescoping for Holonomic Functions (English)

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Christoph Koutschan

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Texts & Monographs in Symbolic Computation

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publication date

1 April 2015

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full work available at URL

https://arxiv.org/abs/1307.4554

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MaRDI profile type

MaRDI publication profile

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When does Zeilberger's algorithm succeed?

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A criterion for the applicability of Zeilberger's algorithm to rational functions

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The method of differentiating under the integral sign

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Hypergeometric series acceleration via the WZ method

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A pretty binomial identity

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THE ITERATED INTEGRALS OF <font>ln</font>(1 + x<sup>n</sup>)

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Some questions concerning computer-generated proofs of a binomial double- sum identity

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Plane partitions. VI: Stembridge's TSPP theorem

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Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory

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Hypergeometric summation algorithms for high-order finite elements

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A computer proof of a polynomial identity implying a partition theorem of Göllnitz

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The analytic continuation of generalized functions with respect to a parameter

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Sparse shape functions for tetrahedral \(p\)-FEM using integrated Jacobi polynomials

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Sparsity optimized high order finite element functions for \(H(\mathrm{curl})\) on tetrahedra

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Algorithms for \(q\)-hypergeometric summation in computer algebra

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Complexity of creative telescoping for bivariate rational functions

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Explicit formula for the generating series of diagonal 3D rook paths

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Ising<i>n</i>-fold integrals as diagonals of rational functions and integrality of series expansions

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Hermite reduction and creative telescoping for hyperexponential functions

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Creative telescoping for rational functions using the griffiths

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A Macsyma implementation of Zeilberger's fast algorithm

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Order-degree curves for hypergeometric creative telescoping

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Trading order for degree in creative telescoping

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Residues and telescopers for bivariate rational functions

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A telescoping method for double summations

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On the existence of telescopers for mixed hypergeometric terms

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Telescopers for rational and algebraic functions via residues

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An extension of Zeilberger's fast algorithm to general holonomic functions

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Non-commutative elimination in Ore algebras proves multivariate identities

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A non-holonomic systems approach to special function identities

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Third order integrability conditions for homogeneous potentials of degree −1

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Irreducibility of \(q\)-difference operators and the knot \(7_{4}\)

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The colored Jones function is \(q\)-holonomic

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THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS

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Generators of some Ramanujan formulas

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Proving hypergeometric identities by numerical verifications

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Zeilberger's holonomic ansatz for Pfaffians

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Non-commutative Gröbner bases in algebras of solvable type

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Summation algorithms for Stirling number identities

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The Holonomic Toolkit

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The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates

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Automated proofs for some Stirling number identities

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Algorithms for \(m\)-fold hypergeometric summation

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REDUCE package for the indefinite and definite summation

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Representations of orthogonal polynomials

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On Zeilberger's algorithm and its \(q\)-analogue

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Identities of nonterminating series by Zeilberger's algorithm

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Advanced applications of the holonomic systems approach

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Eliminating Human Insight: An Algorithmic Proof of Stembridge's TSPP Theorem

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A fast approach to creative telescoping

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Lattice Green functions of the higher-dimensional face-centered cubic lattices

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Advanced computer algebra for determinants

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Proof of George Andrews’s and David Robbins’s <i>q</i> -TSPP conjecture

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Computer Algebra Meets Finite Elements: An Efficient Implementation for Maxwell’s Equations

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A computer proof of a series evaluation in terms of harmonic numbers

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WZ-style certification and sister celine's technique for abel-type sums

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Sharp upper bounds for the orders of the recurrences output by the Zeilberger and \(q\)-Zeilberger algorithms

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Theory of non-commutative polynomials

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Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type

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A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities

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Relativistic Coulomb Integrals and Zeilberger’s Holonomic Systems Approach. I

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Descendants in heap ordered trees or a triumph of computer algebra

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\texttt{qMultiSum} -- a package for proving \(q\)-hypergeometric multiple summation identities

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Simplifying Multiple Sums in Difference Fields

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A concise formula for generalized two-qubit Hilbert–Schmidt separability probabilities

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Binomial identities -- combinatorial and algorithmic aspects

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MultInt, a MAPLE package for multiple integration by the WZ method

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A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report

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An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)'') multisum/integral identities

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A two-line algorithm for proving terminating hypergeometric identities

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A two-line algorithm for proving \(q\)-hypergeometric identities

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A fast algorithm for proving terminating hypergeometric identities

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A holonomic systems approach to special functions identities

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The method of creative telescoping

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The holonomic ansatz. II: Automatic discovery(!) and proof(!!) of holonomic determinant evaluations

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Recurrence and Pólya Number of General One-Dimensional Random Walks

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An Apéry-like difference equation for Catalan's constant

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Identifiers

zbMATH Open document ID

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10.1007/978-3-7091-1616-6_7

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5244921

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