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Rational functions certify combinatorial identities
Author(s):
Herbert S.
Wilf;
Doron
Zeilberger
Journal:
J. Amer. Math. Soc.
3
(1990),
147-158.
MSC:
Primary 05A19;
Secondary 33C05, 68Q40
MathSciNet review:
1007910
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Additional information
References:
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- [1]
- George E. Andrews, Applications of basic hypergeometric functions, SIAM Rev. 16 (1974), 441-484. MR 0352557 (50:5044)
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- W. N. Bailey, Generalized hypergeometric series, Cambridge Tracts in Mathematics, Vol. 32, Cambridge Univ. Press, London, 1935. (Reprinted by Hafner, New York, 1964.) MR 0185155 (32:2625)
- [3]
- J. E. Björk, Rings of differential operators, North-Holland, Amsterdam, 1979. MR 549189 (82g:32013)
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- Shalosh B. Ekhad, A very short proof of Dixon's theorem, J. Combin. Theory Ser. A (to appear). MR 1051787 (91b:05021)
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- -, Short proofs of two hypergeometric summation formulas of Karlsson, Proc. Amer. Math. Soc. 107 (1989), 1143. MR 1019759 (90j:33005)
- [6]
- Shalosh B. Ekhad and Doron Zeilberger, A 21st century proof of Dougall's hypergeometric sum identity, J. Math. Anal. Appl. (to appear).
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- I. Gessel and D. Stanton, Strange evaluations of hypergeometric series, SIAM J. Math. Anal. 13 (1982), 295-308. MR 647127 (83c:33002)
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- -, Applications of
 -Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc. 277 (1983), 173-201. MR 690047 (84f:33009) - [9]
- R. William Gosper, Jr., Decision procedure for indefinite hypergeometric summation, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), 40-42. MR 0485674 (58:5497)
- [10]
- Henry W. Gould, Combinatorial identities, Morgantown, West Virginia, 1972. MR 0354401 (50:6879)
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- R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete mathematics, Addison-Wesley, Reading, MA, 1989. MR 1397498 (97d:68003)
- [12]
- Herbert S. Wilf, 54 computer-generated proofs of binomial coefficient identities (to appear).
- [13]
- Doron Zeilberger, A holonomic systems approach to special function identities (to appear). MR 1090884 (92b:33014)
- [14]
- -, A fast algorithm for proving terminating hypergeometric identities (to appear).
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- -, The method of creative telescoping (to appear).
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MSC:
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MSC:
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Additional Information:
DOI:
10.1090/S0894-0347-1990-1007910-7
PII:
S0894-0347-1990-1007910-7
Copyright of article:
Copyright
1990,
American Mathematical Society
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