相关论文: On the Existence of Telescopers for Rational Funct…
In this paper, we solve the existence problem of telescopers for rational functions in three discrete variables. We reduce the problem to that of deciding the summability of bivariate rational functions, which has been solved recently. The…
We give necessary and sufficient conditions for the existence of telescopers for rational functions of two variables in the continuous, discrete and q-discrete settings and characterize which operators can occur as telescopers. Using this…
We present a new algorithm for constructing minimal telescopers for rational functions in three discrete variables. This is the first discrete reduction-based algorithm that goes beyond the bivariate case. The termination of the algorithm…
We show that the problem of constructing telescopers for functions of m variables is equivalent to the problem of constructing telescopers for algebraic functions of m -1 variables and present a new algorithm to construct telescopers for…
For given multivariate functions specified by algebraic, differential or difference equations, the separability problem is to decide whether they satisfy linear differential or difference equations in one variable. In this paper, we will…
Creative telescoping algorithms compute linear differential equations satisfied by multiple integrals with parameters. We describe a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of…
We present a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on multiplicative and additive decompositions. The criterion enables us to determine the termination of Zeilberger's algorithms for mixed…
The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain…
This paper is a plea for diagonals and telescopers of rational, or algebraic, functions using creative telescoping, in a computer algebra experimental mathematics learn-by-examples approach. We show that diagonals of rational functions (and…
Telescopers for a function are linear differential (resp. difference) operators annihilated by the definite integral (resp. definite sum) of this function. They play a key role in Wilf-Zeilberger theory and algorithms for computing them…
We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approaches, our algorithm has the important feature that the computation of a telescoper is…
Usually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a parameterized telescoping solution, proves algebraic…
Creative telescoping is a powerful computer algebra paradigm -initiated by Doron Zeilberger in the 90's- for dealing with definite integrals and sums with parameters. We address the mixed continuous-discrete case, and focus on the…
Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite…
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of…
We show that the results we had obtained on diagonals of nine and ten parameters families of rational functions using creative telescoping, yielding modular forms expressed as pullbacked $ _2F_1$ hypergeometric functions, can be obtained,…
Based on a modified version of Abramov-Petkov\v{s}ek reduction, a new algorithm to compute minimal telescopers for bivariate hypergeometric terms was developed last year. We investigate further in this paper and present a new argument for…
We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma…
We show that the number of digits in the integers of a creative telescoping relation of expected minimal order for a bivariate proper hypergeometric term has essentially cubic growth with the problem size. For telescopers of higher order…
Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators.…