@incollection{SB_1991-1992__34__41_0, author = {Cartier, Pierre}, title = {D\'emonstration {\guillemotleft} automatique {\guillemotright} d'identit\'es et fonctions hyperg\'eom\'etriques}, booktitle = {S\'eminaire Bourbaki : volume 1991/92, expos\'es 745-759}, series = {Ast\'erisque}, note = {talk:746}, pages = {41--91}, publisher = {Soci\'et\'e math\'ematique de France}, number = {206}, year = {1992}, mrnumber = {1206064}, zbl = {0796.33014}, language = {fr}, url = {http://www.numdam.org/item/SB_1991-1992__34__41_0/} }
TY - CHAP AU - Cartier, Pierre TI - Démonstration « automatique » d'identités et fonctions hypergéométriques BT - Séminaire Bourbaki : volume 1991/92, exposés 745-759 AU - Collectif T3 - Astérisque N1 - talk:746 PY - 1992 SP - 41 EP - 91 IS - 206 PB - Société mathématique de France UR - http://www.numdam.org/item/SB_1991-1992__34__41_0/ LA - fr ID - SB_1991-1992__34__41_0 ER -
%0 Book Section %A Cartier, Pierre %T Démonstration « automatique » d'identités et fonctions hypergéométriques %B Séminaire Bourbaki : volume 1991/92, exposés 745-759 %A Collectif %S Astérisque %Z talk:746 %D 1992 %P 41-91 %N 206 %I Société mathématique de France %U http://www.numdam.org/item/SB_1991-1992__34__41_0/ %G fr %F SB_1991-1992__34__41_0
Cartier, Pierre. Démonstration « automatique » d'identités et fonctions hypergéométriques, in Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Talk no. 746, 51 p. http://www.numdam.org/item/SB_1991-1992__34__41_0/
[1] Handbook of Mathematical functions, Dover, New-York, 1965.
et ,[2] Higher transcendental functions, 3 volumes, McGraw-Hill, New York, 1953.
(éditeur),[3] Table of integrals, series and products, Academic Press, New York, 1980. | Zbl
et ,[4] Fonctions hypergéométriques et hypersphériques, Gauthier-Villars, Paris, 1926. | JFM
et ,[5] Special functions, MacMillan, New York, 1960. | MR | Zbl
,[6] Confluent hypergeometric functions, Cambridge University Press, Cambridge, 1960. | MR | Zbl
,[7] Modern Analysis, Cambridge University Press, Cambridge, 1946.
et ,[8] Combinatorial theory, Springer, Berlin, 1979 (voir surtout le chapitre 3). | MR | Zbl
,[9] The theory of partitions, Addison-Wesley, Reading, 1976. | MR | Zbl
,[10] Advanced Combinatorics, Reidel, Dordrecht, 1974. ¿ | MR | Zbl
,[11] Concrete Mathematics, Addison-Wesley, Reading, 1989. | MR | Zbl
, et ,[12] The art of computer programming, 3 volumes, Addison-Wesley, Reading, 1968-1973. | MR | Zbl
,[13] Combinatory analysis, 2 volumes, Chelsea, New York, 1960 (réimpression). | MR | Zbl
,[14] An introduction to combinatorial analysis, John Wiley, New York, 1958. | MR | Zbl
,[15] q-series : Their development and application in analysis, number theory, combinatorics, physics and computer algebra,CBMS Regional Conference Lecture Series, 66, Amer. Math. Soc., Providence, 1986. | MR | Zbl
,[16] Generalized hypergeometric series, Cambridge University Press, Cambridge, 1935 (réimprimé par Stechert-Hafner, New York, 1964). | MR | Zbl
,[17] q-hypergeometric functions and applications, Ellis Horwood/John Wiley, New York, 1983. | MR | Zbl
,[18] Basic hypergeometric series and applications, Math. Surv. 27, Amer. Math. Soc., Providence, 1988. | MR | Zbl
,[19] Basic hypergeometric series, Cambridge University Press, Cambridge, 1990. | MR | Zbl
et ,[20] Handbuch der Kugelfunktionen. Theorie und Anwendung, 2 volumes, Springer, 1898 (=Physica Verlag, Würzburg, 1961). | MR | Zbl
,[21] Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966. | MR | Zbl
,[1] Sister Celine's technique and its generalizations, J. Math. Anal. Appl. 85 (1982), 114-145. | MR | Zbl
,[2] A Holonomic systems approach to special functions identities, J. of Computational and Applied Math. 32 (1990), 321-368. | MR | Zbl
,[3] A Fast Algorithm for proving terminating hypergeometric identities, Discrete Math. 80 (1990), 207-211. | MR | Zbl
,[4] The method of creative telescoping, J. Symbolic Computation 11 (1991). 195-204. | MR | Zbl
.[5] Closed Form (pun intended !), to appear in : "Special volume in memory of Emil Grosswald", M. Knopp, ed., Contemporary Mathematics, AMS. | MR | Zbl
,[6] Three recitations on Holonomic Systems and Hypergeometric Series, Proceedings of the Séminaire Lotharingien de combinatoire 24, IRMA, Strasbourg, à paraître. | Zbl
,[7] Plain (Lagrange interpolation) proofs of Fancy (representation theory) formulas, en préparation.
,[8] Short proofs of two hypergeometric summation formulas of Karlsson, Proc. Amer. Math. Soc. 107 (1989), 1143-1144. | MR | Zbl
,[9] A very short proof of Dixon's theorem, J. Comb. Theo., Series A 54 (1990), 141-142. | MR | Zbl
,[10] A one-line proof o f the Habsieger-Zeilberger G2 constant term identity, J. Comput. Appl. Math. 34 (1991), 133-134. | MR | Zbl
,[11] Short Proof Of A "Strange" Combinatorial Identity Conjectured by Gosper, Discrete Math. à paraître. | Zbl
,[12] A Short, Elementary and Easy. WZ proof of the Askey-Gasper inequality that was used by de Branges in his proof of the Bieberbach conjecture, à paraître. | Zbl
,[13] A purely verification proof of the first Rogers-Ramanujan identity, J. Comb. The. Ser. A 54 (1990), 309-311. | MR | Zbl
and ,[14] A 21st century proof of Dougall's hypergeometric sum identity, J. Math. Anal. Appl. 147 (1990), 610- 611. | MR | Zbl
and ,[15] Towards computerized proofs of identities, Bulletin of the Amer. Math. Soc. 23 (1990), 77-83. | MR | Zbl
and ,[16] Rational functions certify combinatorial identities, J. Amer. Math. Soc. 3 (1990), 147-158. | MR | Zbl
and ,[17] A general theory of multi-variate hypergeometric identities. en préparation.
and ,[18] 54 computer-generated proofs of binomial coefficient identities, à paraître.
,[19] The method of differentiating under the integral sign, Journ. Symb. Computation, 10 (1990), 571- 591. | MR | Zbl
et ,[20] A MAPLE program that finds, and proves, recurrences and differential equations satisfied by hyperexponential definite integrals, SIGSAM Bulletin 25 (1991),...
et ,[21] A MAPLE program for proving hypergeometric series, SIGSAM Bulletin 25 (1991),...
,[1] Modules over the ring of differential operators. A study of the fundamental solutions of equations with constant coefficients, Funk. Analisis, Akademia Nauk CCCR 5 (2) (1971), 1-16. | MR | Zbl
,[2] The analytic continuation of generalized functions with respect to a parameter, Funct. Anal. and Appl. 6 (1972), 273- 285. | MR | Zbl
,[3] Rings of Differential Operators, North Holland, Amsterdam, 1979. | MR | Zbl
,[4] Algebraic D-modules, Perspectives in Math. 2, Academic Press, Boston, 1987. | MR | Zbl
et al.,[5] An algorithmic method in polynomial ideal theory, N.K. Bose ed. Recents trends in multidimensional systems theory, D. Reidel Publishing Corp., 1985. | MR | Zbl
,[6] The Weyl Algebra, Chapitre V de [4], 173-205.
,[7] Some algorithmic questions on ideals of differential operators, Lect. Note in Comp. Sci. 204 (1985), 413-421. | MR | Zbl
,[8] Decision procedure for indefinite hypergeometric summation, Proc. Nat. Acad. Sci. USA 75 (1978), 40-42. | MR | Zbl
,[9] B-functions and holonomic systems, Invent. Math. 38 (1976), 33-53. | MR | Zbl
,[10] Vanishing cycles sheaves and holonomic systems of differential equations, Springer Lect. Notes in Math. 1016 (1983), 134-142. | MR | Zbl
,[11] L'involutivité des caractéristiques des systèmes différentiels et microdifférentiels, Sém. Bourbaki, exposé 522, 1977-1978 (Lect. Notes in Math. 710, 277-289). | Numdam | MR | Zbl
,[12] The solution of the problem in integrating in finite terms, Bull. Amer. Math. Soc. 76 (1970), 605-608. | MR | Zbl
,[13] Gröbner basis and the problem of contiguous relations, Japan Journ. Appl. Math. 6 (1989), 147-160. | MR | Zbl
,[14] An algorithm for constructing the integral o f a module - an infinite dimensional analog of Gröbner basis, Proceedings of ISSAC'90, A.C.M. Press.
,[15] An approach to the zero recognition problem by Buchberger algorithm, Journ. Symb. Computation, | Zbl
,[1] A note on holonomic q-difference systems, Algebraic Analysis (in honor of M. Sato), M. Kashiwara and T. Kawai eds., Academic Press, (1988), 25-28. | MR | Zbl
,[2] q-analogue of de Rham cohomology associated with Jackson integrals, Proc. Japan Acad. 66 (1990), 161-164. | MR | Zbl
,[3] Finiteness of a cohomology associated with certain Jackson integrals, Tohoku J. Math. 43 (1991), 75-101. | MR | Zbl
,[4] Systèmes holonomes d'équations aux q-différences, Pré-publication Centre de Math. Ecole Polytechnique, Palaiseau, 1991.
,[1] Problèmes combinatoires de commutation et réarrangements, Lect. Notes Math. vol. 85, Springer 1969. | MR | Zbl
et ,[2] Irrationalité de ζ(2) et ζ(3), Astérisque61 (1979), 11-13. | Numdam | Zbl
,[3] A proof that Euler missed... Apery's proof of the irrationality of ζ(3), Math. Intelligencer, 1 (1979), 195-203. Sur les conjectures de Macdonald : | Zbl
,[4] Affine root systems and Dedekind -function, Invent. Math. 15 (1972), 91-143. | Zbl
,[5] Some conjectures for root systems, SIAM Journ. Math. Anal. 13 (1982), 988-1007. | MR | Zbl
,[6] Unified approach to MacDonald's root system conjectures, SIAM Journ. Math. Anal. 19 (1988), 987-1013. | MR | Zbl
,[7] MacDonald's constant term conjectures for exceptional root systems, Bull. Amer. Math. Soc. 24 (1991), 343-347. | MR | Zbl
et ,[8] L'identité de Barnes pour les corps finis, C.R. Acad. Sci. Paris, Série A, 286 (1978), 297-300. | MR | Zbl
,[9] A character sum evaluation and Gaussian hypergeometric series, Journ. Number Theory, 23 (1986), 136-148. | MR | Zbl
et ,