Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Rational function certification of multisum/integral/``$ q$'' identities

Author(s): Herbert S. Wilf; Doron Zeilberger
Journal: Bull. Amer. Math. Soc. 27 (1992), 148-153.
MSC (2000): Primary 11B65; Secondary 05A19, 05A30, 33D99
MathSciNet review: 1145580
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: The method of rational function certification for proving terminating hypergeometric identities is extended from single sums or integrals to multi-integral/sums and "q" integral/sums.

References:

[AZ]
G. Almkvist and D. Zeilberger, The method of differentiating under the integral sign, J. Symbolic Comp. 10 (1990), 571-591. MR 1087980 (92d:26003)

[An]
G. E. Andrews, q-Series: their development and applications in analysis, number theory, combinatorics, physics and computer algebra, CBMS Series, vol. 66, Amer. Math. Soc, Providence, RI, 1986. MR 858826 (88b:11063)

[Ap]
R. Apéry, Irrationalité de $ \zeta $(3), Asterisque 61 (1979), 11-13.

[As1]
R. A. Askey, Orthogonal polynomials and special functions, Regional Conference Series in Appl. Math., vol. 21, SIAM, 1975. MR 0481145 (58:1288)

[As2]
-, Special functions: Group theoretical aspects and applications (preface) (R. A. Askey, T. H. Koornwinder, and W. Schempp, eds.), D. Reidel Publ. Co., Dordrecht, 1984. MR 774053 (85i:22003)

[deB]
L. deBranges, A proof of the Bieberbach conjecture, Acta. Math. 154 (1985), 137-152. MR 772434 (86h:30026)

[CC]
T.-W. Chou and G. E. Collins, Algorithms for the solution of systems of linear Diophantine equations, SIAM J. Comp. 11 (1982), 687-708. MR 677662 (84e:10020)

[Fa]
Sister M. C. Fasenmyer, Some generalized hypergeometric polynomials, Bull. Amer. Math. Soc. 53 (1947), 806-812. MR 0022276 (9:184b)

[Fo]
D. Foata, Combinatoire des identites sur les polynomes orthogonaux, in Proc. ICM, Warsaw, Aug. 16-24, 1983, Varsovie, 1983, pp. 1541-1553. MR 804795 (87a:05020)

[GG]
F. G. Garvan and G. Gonnet, Macdonald's constant term identities for exceptional root systems, Bull. Amer. Math. Soc. 24 (1991), 343-347. MR 1078471 (92b:33054)

[GKZ]
I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Generalized Euler integrals and A-hypergeometric functions, Adv. Math. 84 (1990), 255-271. MR 1080980 (92e:33015)

[Gu]
R. A. Gustafson, A generalization of Selberg's beta integral, Bull. Amer. Math. Soc. (N.S.) 22 (1990), 97-105. MR 1001607 (90j:33001)

[Ma]
I. G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal. 13 (1982), 91-143. MR 674768 (84h:17006a)

[Mi]
W. Miller, Symmetry and separation of variables, Encyclopedia Math. Appl., vol. 4, Addison-Wesley, London, 1977. MR 0460751 (57:744)

[PBM]
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and series, vol. 3 (translated from Russian by G. G. Gould), Gordon and Breach, New York, 1990. MR 1054647 (91c:33001)

[R]
E. D. Rainville, Special functions (reprinted by Chelsea, Bronx, 1971), Macmillan Co., New York, 1960. MR 0107725 (21:6447)

[V]
P. Verbaeten, The automatic construction of pure recurrence relations, Proc. EUROSAM '74, ACM-SIGSAM Bull. 8 (1974), 96-98.

[W]
H. S. Wilf, Finding the kernel of a symbolic matrix, preprint.

[WZ1]
H. S. Wilf and D. Zeilberger, Rational functions certify combinatorial identities, J. Amer. Math. Soc. 3 (1990), 147-158. MR 1007910 (91a:05006)

[WZ2]
-, Towards computerized proofs of identities, Bull. Amer. Math. Soc. 23 (1990), 77-84. MR 1019401 (91a:33003)

[WZ3]
-, An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities, Inventiones Math, (to appear).

[Z1]
D. Zeilberger, A holonomic systems approach to special functions identities, J. Comp. Appl. Math. 32 (1990), 321-368. MR 1090884 (92b:33014)

[Z2]
-, A fast algorithm for proving terminating hypergeometric identities, Discrete Math. 80 (1990), 207-211. MR 1048463 (91d:33006)

[Z3]
-, The method of creative telescoping, J. Symbolic Comp. 11 (1991), 195-204. MR 1103727 (92c:33005)

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 11B65, 05A19, 05A30, 33D99

Retrieve articles in all Journals with MSC (2000): 11B65, 05A19, 05A30, 33D99

Additional Information:

DOI: 10.1090/S0273-0979-1992-00297-5
PII: S 0273-0979(1992)00297-5
Keywords: Identities, hypergeometric, holonomic, recurrence relation, q-sums, multisums, constant term identities, Selberg and Mehta-Dyson integrals
Copyright of article: Copyright 1992, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia