S. A. Abramov, EG-eliminations, Journal of Difference Equations and Applications, vol.50, issue.429, pp.393-433, 1999.
DOI : 10.1007/BF01191378

S. A. Abramov and K. Y. Kvashenko, Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients, Proceedings of the 1991 international symposium on Symbolic and algebraic computation , ISSAC '91, pp.267-270, 1991.
DOI : 10.1145/120694.120735

S. A. Abramov and M. Petkov?ek, Minimal decomposition of indefinite hypergeometric sums, Proceedings of the 2001 international symposium on Symbolic and algebraic computation , ISSAC '01, pp.7-14, 2001.
DOI : 10.1145/384101.384103

S. A. Abramov and M. Van-hoeij, Integration of solutions of linear functional equations, Integral Transforms and Special Functions, vol.34, issue.6, pp.3-12, 1999.
DOI : 10.2307/1968173

K. Adjamagbo, Sur l'effectivité du lemme du vecteur cyclique, C. R. Acad. Sci. Paris Sér. I Math, vol.306, issue.13, pp.543-546, 1988.

A. Adolphson, An index theorem for p-adic differential operators, Trans. Amer. Math. Soc, vol.216, pp.279-293, 1976.
DOI : 10.2307/1997699

G. Almkvist and D. Zeilberger, The method of differentiating under the integral sign, Journal of Symbolic Computation, vol.10, issue.6, pp.571-591, 1990.
DOI : 10.1016/S0747-7171(08)80159-9

M. A. Barkatou, On Rational Solutions of Systems of Linear Differential Equations, Journal of Symbolic Computation, vol.28, issue.4-5, pp.547-567, 1999.
DOI : 10.1006/jsco.1999.0314

A. Bostan, S. Chen, F. Chyzak, and Z. Li, Complexity of creative telescoping for bivariate rational functions Hermite reduction and creative telescoping for hyperexponential functions, ISSAC'10 ISSAC'13, pp.203-210, 2010.

A. Bostan, L. Dumont, and B. Salvy, Efficient algorithms for mixed creative telescoping, ISSAC'16, pp.127-134, 2016.
DOI : 10.1145/2930889.2930907
URL : https://hal.archives-ouvertes.fr/hal-01317940

A. Bostan, P. Lairez, and B. Salvy, Creative telescoping for rational functions using the Griffiths-Dwork method, ISSAC'13, pp.93-100, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00777675

S. Chen, H. Huang, M. Kauers, and Z. Li, A Modified Abramov-Petkovsek Reduction and Creative Telescoping for Hypergeometric Terms, Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '15, pp.117-124, 2015.
DOI : 10.1016/S0747-7171(08)80044-2
URL : http://arxiv.org/pdf/1501.04668

S. Chen, M. Kauers, and C. Koutschan, Reduction-Based Creative Telescoping for Algebraic Functions, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '16, pp.175-182, 2016.
DOI : 10.1016/S0747-7171(08)80044-2
URL : http://arxiv.org/pdf/1602.00424

S. Chen, M. Kauers, and M. F. Singer, Telescopers for rational and algebraic functions via residues, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.130-137, 2012.
DOI : 10.1145/2442829.2442851
URL : http://arxiv.org/pdf/1201.1954.pdf

S. Chen, M. Van-hoeij, M. Kauers, and C. Koutschan, Reduction-based creative telescoping for fuchsian D-finite functions, Journal of Symbolic Computation, vol.85, pp.108-127, 2018.
DOI : 10.1016/j.jsc.2017.07.005

R. C. Churchill and J. J. Kovacic, CYCLIC VECTORS, Differential Algebra and Related Topics, pp.191-218, 2002.
DOI : 10.1142/9789812778437_0007

F. Chyzak, Fonctions holonomes en calcul formel, 1998.
URL : https://hal.archives-ouvertes.fr/tel-00991717

F. Chyzak, 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

F. Chyzak, The ABC of Creative Telescoping ? Algorithms, Bounds, Complexity. Accreditation to supervise research (HDR), École polytechnique, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01069831

F. Chyzak and B. Salvy, Non-commutative Elimination in Ore Algebras Proves Multivariate Identities, Journal of Symbolic Computation, vol.26, issue.2, pp.187-227, 1998.
DOI : 10.1006/jsco.1998.0207
URL : https://hal.archives-ouvertes.fr/inria-00073891

J. H. Davenport, The Risch Differential Equation Problem, SIAM Journal on Computing, vol.15, issue.4, pp.903-918, 1986.
DOI : 10.1137/0215063

L. E. Dickson, Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors, American Journal of Mathematics, vol.35, issue.4, pp.413-422, 1913.
DOI : 10.2307/2370405

J. C. Faugère, P. Gianni, D. Lazard, and T. Mora, Efficient Computation of Zero-dimensional Gr??bner Bases by Change of Ordering, Journal of Symbolic Computation, vol.16, issue.4, pp.329-344, 1993.
DOI : 10.1006/jsco.1993.1051

L. Fuchs, Die Periodicitätsmoduln der hyperelliptischen Integrale als Functionen eines Parameters aufgefasst, J. Reine Angew. Math, vol.71, pp.91-127, 1870.
DOI : 10.1515/crll.1870.71.91

K. Geddes, H. Le, and Z. Li, Differential rational normal forms and a reduction algorithm for hyperexponential functions, ISSAC'04, pp.183-190, 2004.

C. Hermite, Sur l'int??gration des fractions rationnelles, Annales scientifiques de l'??cole normale sup??rieure, vol.1, issue.2, pp.215-218
DOI : 10.24033/asens.82

H. Huang, New Bounds for Hypergeometric Creative Telescoping, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '16, pp.279-286, 2016.
DOI : 10.1016/S0747-7171(08)80044-2
URL : http://arxiv.org/pdf/1604.08059

E. L. Ince, Ordinary Differential Equations, The Mathematical Gazette, vol.18, issue.231, 1944.
DOI : 10.2307/3605524

C. Koutschan, Advanced applications of the holonomic systems approach, ACM SIGSAM Bulletin, vol.43, issue.3/4, 2009.
DOI : 10.1145/1823931.1823954

P. Lairez, Computing periods of rational integrals, Mathematics of Computation, vol.85, issue.300, pp.1719-1752, 2016.
DOI : 10.1090/mcom/3054
URL : https://hal.archives-ouvertes.fr/hal-01097145

J. Liouville, Second mémoire sur la détermination des intégrales dont la valeur est algébrique, pp.149-193, 1833.

L. Lipshitz, The diagonal of a D-finite power series is D-finite, Journal of Algebra, vol.113, issue.2, pp.373-378, 1988.
DOI : 10.1016/0021-8693(88)90166-4

B. Malgrange, Sur les points singuliers des équations différentielles, Enseignement Math, vol.20, issue.2, pp.147-176, 1974.

P. Monsky, Finiteness of De Rham Cohomology, American Journal of Mathematics, vol.94, issue.1, pp.237-245, 1972.
DOI : 10.2307/2373603

M. Ostrogradsky, De l'intégration des fractions rationnelles. Bull. classe phys, math . Acad. Impériale des Sciences Saint-Pétersbourg, pp.145-167

É. Picard, Sur les intégrales doubles de fonctions rationnelles dont tous les résidus sont nuls, Bull. Sci. Math, vol.26, issue.2, pp.143-152, 1902.

É. Picard and G. Simart, Théorie des fonctions algébriques de deux variables indépendantes , volume I (1897) and II Gauthier-Villars et fils, 1897.

M. S. Rezaoui, Indice polynomial d'une matrice d'op??rateurs diff??rentiels, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.6, pp.505-508, 2001.
DOI : 10.1016/S0764-4442(01)01906-1

N. Takayama, An approach to the zero recognition problem by Buchberger algorithm, Journal of Symbolic Computation, vol.14, issue.2-3, pp.265-282, 1992.
DOI : 10.1016/0747-7171(92)90039-7

B. M. Trager, Integration of Algebraic Functions, 1984.

J. Van-der-hoeven, Constructing reductions for creative telescoping, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01435877

M. Van-der-put and M. Reversat, A local-global problem for linear differential equations, Pacific Journal of Mathematics, vol.102, issue.1, pp.171-199, 2008.
DOI : 10.1007/978-1-4612-1126-6
URL : https://hal.archives-ouvertes.fr/hal-00635471

M. Van-der-put and M. F. Singer, Galois theory of linear differential equations, 2003.
DOI : 10.1007/978-3-642-55750-7

D. Y. Yun, On square-free decomposition algorithms, Proceedings of the third ACM symposium on Symbolic and algebraic computation , SYMSAC '76, pp.26-35, 1976.
DOI : 10.1145/800205.806320

D. Y. Yun, Fast algorithm for rational function integration, Proc. IFIP'77 Congr, pp.493-498, 1977.