93 citations · 692 across the 41 of their papers we have counts for
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Reduction-Based Creative Telescoping for Definite Summation of D-finite Functions
Hadrien Brochet, Bruno Salvy
Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative…
Positivity certificates for linear recurrences
Alaa Ibrahim, Bruno Salvy
We consider linear recurrences with polynomial coefficients of Poincaré type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity…
Minimization of differential equations and algebraic values of -functions
Alin Bostan, Tanguy Rivoal, Bruno Salvy
A power series being given as the solution of a linear differential equation with appropriate initial conditions, minimization consists in finding a non-trivial linear differential…
Effective Coefficient Asymptotics of Multivariate Rational Functions via Semi-Numerical Algorithms for Polynomial Systems
Stephen Melczer, Bruno Salvy
The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic proper…
Linear Differential Equations as a Data-Structure
Bruno Salvy
A lot of information concerning solutions of linear differential equations can be computed directly from the equation. It is therefore natural to consider these equations as a data…
Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions
Alin Bostan, Frédéric Chyzak, Pierre Lairez +1
Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the deriva…