Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory
From MaRDI portal
Publication:863306
DOI10.1016/j.aam.2005.09.003zbMath1108.05010OpenAlexW2063489833MaRDI QIDQ863306
Publication date: 26 January 2007
Published in: Advances in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.aam.2005.09.003
Related Items
Exploring general Apéry limits via the Zudilin–Straub t-transform ⋮ Analysis of the gift exchange problem ⋮ Comments on Risch’s On the Integration of Elementary Functions which are Built Up Using Algebraic Operations ⋮ A supercongruence involving Delannoy numbers and Schröder numbers ⋮ Elementary proof of congruences involving sum of binomial coefficients ⋮ Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals ⋮ Calculating three loop ladder and \(V\)-topologies for massive operator matrix elements by computer algebra ⋮ Multiple binomial sums ⋮ A generalized supercongruence of Kimoto and Wakayama ⋮ Proof of some divisibility results on sums involving binomial coefficients ⋮ Analytic computing methods for precision calculations in quantum field theory ⋮ Some open problems related to creative telescoping ⋮ An algorithmic approach to the \(q\)-summability problem of bivariate rational functions ⋮ Using the “Freshman′s Dream” to Prove Combinatorial Congruences ⋮ Summations of linear recurrent sequences ⋮ The three-loop splitting functions \(P_{q g}^{(2)}\) and \(P_{g g}^{(2, \operatorname{N}_{\operatorname{F}})}\) ⋮ Tweaking the Beukers integrals in search of more miraculous irrationality proofs a la Apéry ⋮ The polarized three-loop anomalous dimensions from on-shell massive operator matrix elements ⋮ An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process ⋮ Counting condorcet ⋮ The first-order factorizable contributions to the three-loop massive operator matrix elements \(A_{Qg}^{(3)}\) and \(\Delta A_{Qg}^{(3)}\) ⋮ Trading order for degree in creative telescoping ⋮ Egorychev method: a hidden treasure ⋮ Series evaluation of a quartic integral ⋮ A symbolic summation approach to Feynman integral calculus ⋮ Rational approximations to values of the digamma function and a conjecture on denominators ⋮ The 1958 Pekeris-Accad-WEIZAC ground-breaking collaboration that computed ground states of two-electron atoms (and its 2010 redux) ⋮ No-neighbours recurrence schemes for space-time Green’s functions on a 3D simple cubic lattice ⋮ Summation theory. II: Characterizations of \(R {\Pi}{\Sigma}^{\ast}\)-extensions and algorithmic aspects ⋮ Minimal representations and algebraic relations for single nested products ⋮ The quasi-holonomic ansatz and restricted lattice walks ⋮ The transition matrix element \(A_{gq}(N)\) of the variable flavor number scheme at \(O({\alpha}_s^3)\) ⋮ The polarized transition matrix element \(A_{gq}(N)\) of the variable flavor number scheme at \(O(\alpha_s^3)\) ⋮ Congruences on sums of super Catalan numbers ⋮ A note on moments of limit log-infinitely divisible stochastic measures of Bacry and Muzy ⋮ A symbolic computation approach to a problem involving multivariate Poisson distributions ⋮ An algorithm for deciding the summability of bivariate rational functions ⋮ Logarithmic and Complex Constant Term Identities ⋮ Holonomic gradient descent and its application to the Fisher-Bingham integral ⋮ A recursive method to calculate the expected molecule numbers for a polymerization network with a small number of subunits ⋮ A telescoping method for double summations ⋮ The computational challenge of enumerating high-dimensional rook walks ⋮ Computing periods of rational integrals ⋮ Revitalized automatic proofs: demonstrations ⋮ Supercongruences for truncated Appell series ⋮ Identities in character tables ofSn ⋮ THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS ⋮ Large Scale Analytic Calculations in Quantum Field Theories ⋮ MultiZeilberger ⋮ A remarkable sequence of integers ⋮ Automatic discovery of irrationality proofs and irrationality measures ⋮ Creative Telescoping for Holonomic Functions ⋮ Simplifying Multiple Sums in Difference Fields ⋮ Linear differential equations as a data structure ⋮ Positivity of rational functions and their diagonals ⋮ A by-product of an integral evaluation ⋮ APÉRY LIMITS FOR ELLIPTIC -VALUES ⋮ Analytic Integration Methods in Quantum Field Theory: An Introduction ⋮ Extensions of the AZ-Algorithm and the Package MultiIntegrate ⋮ Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation ⋮ The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals
Uses Software
Cites Work
- The method of differentiating under the integral sign
- An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
- Combinatorial sums, identities and trace identities of the 2x2 matrices
- Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type
- MultInt, a MAPLE package for multiple integration by the WZ method
- Sharp upper bounds for the orders of the recurrences output by the Zeilberger and \(q\)-Zeilberger algorithms
- Some Conjectures for Root Systems
