On the summation of P -recursive sequences, Proceedings of the international symposium on symbolic and algebraic computation. ISSAC '06, pp.17-22, 2006. ,
D'Alembertian solutions of linear differential and difference equations, Proceedings of the international symposium on Symbolic and algebraic computation , ISSAC '94, pp.169-174, 1994. ,
DOI : 10.1145/190347.190412
Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula, Proceedings of the 2005 international symposium on Symbolic and algebraic computation , ISSAC '05, pp.5-12, 2005. ,
DOI : 10.1145/1073884.1073888
Hadamard grade of power series, Journal of Number Theory, vol.131, issue.11, 2011. ,
DOI : 10.1016/j.jnt.2011.04.011
URL : https://hal.archives-ouvertes.fr/hal-01023479
Some Questions Concerning Computer-Generated Proofs of a Binomial Double-Sum Identity, Journal of Symbolic Computation 16.2, pp.147-153, 1038. ,
DOI : 10.1006/jsco.1993.1038
Multi-variable Zeilberger and Almkvist???Zeilberger algorithms and the sharpening of Wilf???Zeilberger theory, Advances in Applied Mathematics, vol.37, issue.2, pp.139-152, 2006. ,
DOI : 10.1016/j.aam.2005.09.003
Integer points in polyhedra, Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), pp.10-4171, 2008. ,
DOI : 10.4171/052
Problem E3376, American Mathematical Monthly, vol.973, p.240, 1990. ,
Creative telescoping for rational functions using the Griffiths-Dwork method, Proceedings of the international symposium on symbolic and algebraic computation. ISSAC '13, pp.93-100, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00777675
-fold integrals as diagonals of rational functions and integrality of series expansions, Journal of Physics A: Mathematical and Theoretical, vol.46, issue.18, pp.185202-185246, 2013. ,
DOI : 10.1088/1751-8113/46/18/185202
URL : https://hal.archives-ouvertes.fr/inria-00139665
Some binomial sums involving absolute values, 2014. ,
Points entiers dans les poly??dres convexes, Annales Scientifiques de l' ´ Ecole Normale Supérieure.Quatrì eme Série 21.4, pp.653-663, 1988. ,
DOI : 10.24033/asens.1572
Analytic continuation of diagonals and Hadamard compositions of multiple power series, Transactions of the American Mathematical Society, vol.44, issue.1, pp.1-7, 1938. ,
DOI : 10.1090/S0002-9947-1938-1501956-3
Problem 11914, American Mathematical Monthly, vol.1235, p.613, 2016. ,
Diagonales de fractions rationnelles etéquationsetéquations de Picard-Fuchs " . In: Study group on ultrametric analysis, 12 th year, 1984. ,
An extension of Zeilberger's fast algorithm to general holonomic functions, Discrete Mathematics, vol.217, issue.1-3, pp.115-134, 2000. ,
DOI : 10.1016/S0012-365X(99)00259-9
A Computer-Algebra-Based Formal Proof of the Irrationality of ?(3), th International Conference on Interactive Theorem Proving, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00984057
Resolution of singularities, Graduate Studies in Mathematics, vol.63, 2004. ,
DOI : 10.1090/gsm/063
New applications of the Egorychev method of coefficients of integral representation and calculation of combinatorial sums, 2015. ,
On the sum of the cubes of the coefficients in a certain expansion by the binomial theorem, pp.79-80, 1891. ,
Integral representation and the computation of combinatorial sums Translations of Mathematical Monographs. Translated from the Russian by, 1984. ,
Integral Representation and Algorithms for Closed Form Summation, Handbook of algebra, vol.5, issue.5, 2008. ,
DOI : 10.1016/S1570-7954(07)05009-7
Coefficients of algebraic series. Tech. rep. 3504. Algorithms seminar 1997-1998. Inria, pp.27-30, 1998. ,
On the Non-Holonomic Character of Logarithms, Powers, and the nth Prime Function, In: Electr. J. Comb, vol.11, issue.2, 2005. ,
Algebraic functions over finite fields, Journal of Algebra, vol.7, issue.2, pp.271-277, 1967. ,
DOI : 10.1016/0021-8693(67)90061-0
G-functions and multisum versus holonomic sequences, Advances in Mathematics, vol.220, issue.6, pp.1945-1955, 2009. ,
DOI : 10.1016/j.aim.2008.11.012
A new algorithm for the recursion of hypergeometric multisums with improved universal denominator, In: Gems in experimental mathematics. Contemp. Math. Providence, vol.517517, pp.143-156, 2010. ,
DOI : 10.1090/conm/517/10138
Counting with irrational tiles, 2014. ,
Concrete Mathematics: A Foundation for Computer Science, Computers in Physics, vol.3, issue.5, 1989. ,
DOI : 10.1063/1.4822863
On the de rham cohomology of algebraic varieties, Institut des HautesÉtudesHautes´HautesÉtudes Scientifiques. Publications Mathématiques 29, pp.95-103, 1966. ,
DOI : 10.1007/BF02684807
Ordinary Differential Equations, The Mathematical Gazette, vol.18, issue.231, 1944. ,
DOI : 10.2307/3605524
Nilpotent connections and the monodromy theorem: Applications of a result of turrittin, Institut des HautesÉtudesHautes´HautesÉtudes Scientifiques. Publications Mathématiques 39, pp.175-232, 1970. ,
DOI : 10.1007/BF02684688
A Fast Approach to Creative Telescoping, Mathematics in Computer Science, vol.32, issue.3, pp.259-266, 2010. ,
DOI : 10.1007/s11786-010-0055-0
Périodes d'intégrales rationnelles : algorithmes et applications, 2014. ,
The diagonal of a D-finite power series is D-finite, Journal of Algebra 113.2, pp.373-378, 1988. ,
DOI : 10.1016/0021-8693(88)90166-4
Effective bounds for P-recursive sequences, Journal of Symbolic Computation 45.10, pp.1075-1096, 2010. ,
DOI : 10.1016/j.jsc.2010.06.024
URL : https://hal.archives-ouvertes.fr/inria-00376219
On ordered division rings, Transactions of the American Mathematical Society, vol.66, issue.1, pp.202-252, 1949. ,
DOI : 10.1090/S0002-9947-1949-0032593-5
A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities, Journal of Symbolic Computation, vol.20, issue.5-6, pp.5-6, 1995. ,
DOI : 10.1006/jsco.1995.1071
Analytic Combinatorics in Several Variables, pp.10-1017, 2013. ,
DOI : 10.1017/CBO9781139381864
Hypergeometric solutions of linear recurrences with polynomial coefficients, Journal of Symbolic Computation, vol.14, issue.2-3, pp.243-264, 1992. ,
DOI : 10.1016/0747-7171(92)90038-6
Algebraically Closed Fields Analogous to Fields of Puiseux Series, Journal of the London Mathematical Society, vol.2, issue.3, pp.504-506, 1974. ,
DOI : 10.1112/jlms/s2-8.3.504
Symbolic-numeric tools for analytic combinatorics in several variables, Proceedings of the international symposium on symbolic and algebraic computation. ISSAC '16, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01310691
GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable, ACM Transactions on Mathematical Software, vol.20, issue.2, pp.163-177, 1994. ,
DOI : 10.1145/178365.178368
URL : https://hal.archives-ouvertes.fr/hal-00917741
Binomial identities ??? combinatorial and algorithmic aspects, Discrete Mathematics, vol.136, issue.1-3, pp.309-346, 1994. ,
DOI : 10.1016/0012-365X(94)00118-3
URL : http://doi.org/10.1016/0012-365x(94)00118-3
An Algorithm for Finding Recurrence Relations of Binomial Sums and its Complexity, Symbolic computation in combinatorics ? 1, pp.5-6, 1993. ,
DOI : 10.1006/jsco.1995.1069
Algebraic Curves, 1950. ,
Computer Generated Proofs of Binomial Multi-Sum Identities, 1997. ,
An algorithmic proof theory for hypergeometric (ordinary and ???q???) multisum/integral identities, Inventiones Mathematicae, vol.54, issue.1, pp.575-633, 1992. ,
DOI : 10.1007/BF02100618
The ring of Malcev-Neumann series and the residue theorem, p.405133, 2004. ,
A holonomic systems approach to special functions identities, Journal of Computational and Applied Mathematics, vol.32, issue.3, pp.321-368, 1990. ,
DOI : 10.1016/0377-0427(90)90042-X
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