Fetching the paper…
Reading the bibliography…
The aim of this article is twofold: on the one hand it is intended to serve as a gentle introduction to the topic of creative telescoping, from a practical point of view; for this purpose its application to several problems is exemplified.
Theory of non-commutative polynomials
Øystein Ore · 1933
Earlier work this paper cites.
Ein Algorithmus zum Auffinden der Basiselemente des Restklassenrings nach einem nulldimensionalen Polynomideal
Bruno Buchberger · 1965
Earlier work this paper cites.
The analytic continuation of generalized functions with respect to a parameter
Joseph N. Bernstein · 1972
Earlier work this paper cites.
A proof that Euler missed—Apéry’s proof of the irrationality of ζ ( 3 ) \zeta(3) . An informal report
Alfred van der Poorten · 1979
Earlier work this paper cites.
Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character
Richard P. Feynman and Ralph Leighton (ed.) · 1985
Earlier work this paper cites.
The method of differentiating under the integral sign
Gert Almkvist and Doron Zeilberger · 1990
Earlier work this paper cites.
Non-commutative Gröbner bases in algebras of solvable type
Abdelilah Kandri-Rody and Volker Weispfenning · 1990
Earlier work this paper cites.
An algorithm of constructing the integral of a module—an infinite dimensional analog of Gröbner basis
Nobuki Takayama · 1990
Earlier work this paper cites.
A fast algorithm for proving terminating hypergeometric identities
Doron Zeiberger · 1990
Earlier work this paper cites.
A holonomic systems approach to special functions identities
Doron Zeilberger · 1990
Earlier work this paper cites.
The method of creative telescoping
Doron Zeilberger · 1991
Earlier work this paper cites.
Démonstration “automatique” d’identités et fonctions hypergéometriques [d’après D. Zeilberger]
Pierre Cartier · 1992
Earlier work this paper cites.
An algorithmic proof theory for hypergeometric (ordinary and “ q q ”) multisum/integral identities
Herbert S. Wilf and Doron Zeilberger · 1992
Earlier work this paper cites.
Some questions concerning computer-generated proofs of a binomial double-sum identity
George E. Andrews and Peter Paule · 1993
Earlier work this paper cites.
On Zeilberger’s algorithm and its q q -analogue
Tom H. Koornwinder · 1993
Earlier work this paper cites.
A WZ proof of Ramanujan’s formula for π \pi
Shalosh B. Ekhad and Doron Zeilberger · 1994
Earlier work this paper cites.
Concrete Mathematics
Ronald L. Graham, Donald E. Knuth, and Oren Patashnik · 1994
Earlier work this paper cites.
Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type
Peter Paule · 1994
Earlier work this paper cites.
Binomial identities—combinatorial and algorithmic aspects
Volker Strehl · 1994
Earlier work this paper cites.
A primer of algebraic D D -modules
Severino C. Coutinho · 1995
Earlier work this paper cites.
Algorithms for m m -fold hypergeometric summation
Wolfram Koepf · 1995
Earlier work this paper cites.
REDUCE package for the indefinite and definite summation
Wolfram Koepf · 1995
Earlier work this paper cites.
A Mathematica version of Zeilberger’s algorithm for proving binomial coefficient identities
Peter Paule and Markus Schorn · 1995
Earlier work this paper cites.
Symbolic summation—some recent developments
Peter Paule and Volker Strehl · 1995
Earlier work this paper cites.
A Mathematica q q -analogue of Zeilberger’s algorithm for proving q q -hypergeometric identities
Axel Riese · 1995
Earlier work this paper cites.
Three recitations on holonomic systems and hypergeometric series
Doron Zeilberger · 1995
Earlier work this paper cites.
WZ-style certification and Sister Celine’s technique for Abel-type sums
John E. Majewicz · 1996
Earlier work this paper cites.
A = B A=B
Marko Petkovšek, Herbert S. Wilf, and Doron Zeilberger · 1996
Earlier work this paper cites.
Descendants in heap ordered trees or a triumph of computer algebra
Helmut Prodinger · 1996
Earlier work this paper cites.
A two-line algorithm for proving terminating hypergeometric identities
Lily Yen · 1996
Earlier work this paper cites.
Hypergeometric series acceleration via the WZ method
Tewodros Amdeberhan and Doron Zeilberger · 1997
Earlier work this paper cites.
Computer generated proofs of binomial multi-sum identities
Kurt Wegschaider · 1997
Earlier work this paper cites.
A two-line algorithm for proving q q -hypergeometric identities
Lily Yen · 1997
Earlier work this paper cites.
Fonctions holonomes en calcul formel
Frédéric Chyzak · 1998
Earlier work this paper cites.
Gröbner bases, symbolic summation and symbolic integration
Frédéric Chyzak · 1998
Earlier work this paper cites.
Non-commutative elimination in Ore algebras proves multivariate identities
Frédéric Chyzak and Bruno Salvy · 1998
Cited alongside, same era.
Hypergeometric Summation. An Algorithmic Approach to Summation and Special Function Identities
Wolfram Koepf · 1998
Cited alongside, same era.
Representations of orthogonal polynomials
Wolfram Koepf and Dieter Schmersau · 1998
Cited alongside, same era.
Identities of nonterminating series by Zeilberger’s algorithm
Tom H. Koornwinder · 1998
Cited alongside, same era.
Algorithms for q q -hypergeometric summation in computer algebra
Harald Böing and Wolfram Koepf · 1999
Cited alongside, same era.
A Macsyma implementation of Zeilberger’s fast algorithm
Fabrizio Caruso · 2000
Cited alongside, same era.
Apéry’s theorem. Thirty years after [an elementary proof of Apéry’s theorem]
Wadim Zudilin · 2009
Later among the works it cites.
Modern summation methods and the computation of 2- and 3-loop Feynman diagrams
Jakob Ablinger, Johannes Blümlein, Sebastian Klein, and Carsten Schneider · 2010
Later among the works it cites.
Complexity of creative telescoping for bivariate rational functions
Alin Bostan, Shaoshi Chen, Frédéric Chyzak, and Ziming Li · 2010
Later among the works it cites.
The non-commutative A A -polynomial of twist knots
Stavros Garoufalidis and Xinyu Sun · 2010
Later among the works it cites.
Eliminating human insight: an algorithmic proof of Stembridge’s TSPP theorem
Christoph Koutschan · 2010
Later among the works it cites.
A fast approach to creative telescoping
Christoph Koutschan · 2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
An extension of Zeilberger’s fast algorithm to general holonomic functions
Frédéric Chyzak · 2000
Cited alongside, same era.
Fine-tuning Zeilberger’s algorithm—the methods of automatic filtering and creative substituting
A. Riese · 2001
Cited alongside, same era.
Symbolic Summation in Difference Fields
Carsten Schneider · 2001
Cited alongside, same era.
A criterion for the applicability of Zeilberger’s algorithm to rational functions
Sergei A. Abramov and Ha Q. Le · 2002
Cited alongside, same era.
A computer proof of a polynomial identity implying a partition theorem of Göllnitz
Alexander Berkovich and A. Riese · 2002
Cited alongside, same era.
A computer proof of a series evaluation in terms of harmonic numbers
Russell Lyons, Peter Paule, and Axel Riese · 2002
Cited alongside, same era.
HolonomicFunctions (user’s guide)
Christoph Koutschan · 2010
Later among the works it cites.
Explicit formula for the generating series of diagonal 3D rook paths
Alin Bostan, Frédéric Chyzak, Mark van Hoeij, and Lucien Pech · 2011
Later among the works it cites.
The Concrete Tetrahedron
Manuel Kauers and Peter Paule · 2011
Later among the works it cites.
Proof of George Andrews’s and David Robbins’s q q -TSPP conjecture
Christoph Koutschan, Manuel Kauers, and Doron Zeilberger · 2011
Later among the works it cites.
The integrals in Gradshteyn and Ryzhik. Part 18: Some automatic proofs
Christoph Koutschan and Victor H. Moll · 2011
Later among the works it cites.
Recurrence and Pólya number of general one-dimensional random walks
Xiao-Kun Zhang, Jing Wan, Jing-Ju Lu, and Xin-Ping Xu · 2011
Later among the works it cites.
A pretty binomial identity
Tewodros Amdeberhan, Valerio de Angelis, Minghua Lin, Victor H. Moll, and B. Sury · 2012
Later among the works it cites.
The iterated integrals of ln ( 1 + x n ) \ln(1+x^{n})
Tewodros Amdeberhan, Christoph Koutschan, Victor H. Moll, and Eric S. Rowland · 2012
Later among the works it cites.
Ising n n -fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity
Alin Bostan, Salah Boukraa, Gilles Christol, Saoud Hassani, and Jean-Marie Maillard · 2012
Later among the works it cites.
On the existence of telescopers for mixed hypergeometric terms
Shaoshi Chen, Frédéric Chyzak, Ruyong Feng, Guofeng Fu, and Ziming Li · 2012
Later among the works it cites.
Order-degree curves for hypergeometric creative telescoping
Shaoshi Chen and Manuel Kauers · 2012
Later among the works it cites.
Trading order for degree in creative telescoping
Shaoshi Chen and Manuel Kauers · 2012
Later among the works it cites.
Telescopers for rational and algebraic functions via residues
Shaoshi Chen, Manuel Kauers, and Michael F. Singer · 2012
Later among the works it cites.
Residues and telescopers for bivariate rational functions
Shaoshi Chen and Michael F. Singer · 2012
Later among the works it cites.
Third order integrability conditions for homogeneous potentials of degree − 1 -1
Thierry Combot and Christoph Koutschan · 2012
Later among the works it cites.
Zeilberger’s holonomic ansatz for Pfaffians
Masao Ishikawa and Christoph Koutschan · 2012
Later among the works it cites.
Computer algebra meets finite elements: an efficient implementation for Maxwell’s equations
Christoph Koutschan, Christoph Lehrenfeld, and Joachim Schöberl · 2012
Later among the works it cites.
Definite Integration in Differential Fields
Clemens G. Raab · 2012
Later among the works it cites.
Sparsity optimized high order finite element functions for H(curl) on tetrahedra
Sven Beuchler, Veronika Pillwein, and Sabine Zaglmayr · 2013
Closest in time.
Hermite reduction and creative telescoping for hyperexponential functions
Alin Bostan, Shaoshi Chen, Frédéric Chyzak, Ziming Li, and Guoce Xin · 2013
Closest in time.
Creative telescoping for rational functions using the Griffiths-Dwork method
Alin Bostan, Pierre Lairez, and Bruno Salvy · 2013
Closest in time.
Irreducibility of q q -difference operators and the knot 7 4 7_{4}
Stavros Garoufalidis and Christoph Koutschan · 2013
Closest in time.
The holonomic toolkit
Manuel Kauers · 2013
Closest in time.
Lattice Green’s functions of the higher-dimensional face-centered cubic lattices
Christoph Koutschan · 2013
Closest in time.
Advanced computer algebra for determinants
Christoph Koutschan and Thotsaporn Thanatipanonda · 2013
Closest in time.
Relativistic Coulomb integrals and Zeilbergers holonomic systems approach I
Peter Paule and Sergei Suslov · 2013
Closest in time.
Simplifying multiple sums in difference fields
Carsten Schneider · 2013
Closest in time.
A concise formula for generalized two-qubit Hilbert-Schmidt separability probabilities
Paul B. Slater · 2013
Closest in time.