|
Towards computerized proofs of identities
Author(s):
Herbert S.
Wilf;
Doron
Zeilberger
Journal:
Bull. Amer. Math. Soc.
23
(1990),
77-83.
MSC (1985):
Primary 05A19
MathSciNet review:
1019401
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- 1.
- G. E. Andrews, Applications of basic hypergeometric functions, SIAM Rev. 16 (1974), 441-484. MR 352557
- 2.
- W. N. Bailey, Generalized hypergeometric series, Cambridge Tracts in Mathematics, vol. 32, Cambridge University Press, London, 1935. (Reprinted by Hafner, New York, 1964.) MR 185155
- 3.
- I. N. Bernstein, Modules over a ring of differential operators, study of the fundamental solutions of equations with constant coefficients, Functional Anal. Appl. 5 (1974), 89-101.
- 4.
- I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Functional Anal. Appl. 6 (1972), 273-285. MR 320735
- 5.
- G. D. Birkhoff and W. J. Trjitzinsky, Analytic theory of singular difference equations, Acta Math. 60 (1932), 1-8.
- 6.
- J. E. Björk, Rings of differential operators, North-Holland, Amsterdam, 1979. MR 549189
- 7.
- S. B. Ekhad and S. Tre, A purely verification proof of the first Rogers Ramanujan identity, J. Combin. Theory Ser. A. (to appear). MR 1060003
- 8.
- A. Erdélyi et al, The higher transcendental functions, (3 vols.), McGraw-Hill, New York, 1953.
- 9.
- I. Gessel and D. Stanton, Strange evaluations of hypergeometric series, SIAM J. Math. Anal. 13 (1982), 295-308. MR 647127
- 10.
- R. W. Gosper, Jr., Decision procedure for indefinite hypergeometric summation, Proc. Nat. Acad. Sci. USA 75 (1978), 40-42. MR 485674
- 11.
- H. W. Gould, Combinatorial identities, Morgantown, WV, 1972. MR 354401
- 12.
- R. L. Graham, D. E. Knuth and O. Patashnik, Concrete mathematics, Addison-Wesley, Reading, MA, 1989. MR 1397498
- 13.
- E. D. Rainville, Special functions, Chelsea, Bronx, New York, 1971. (Originally published by Macmillan, 1960.) MR 107725
- 14.
- R. H. Risch, The solution of the problem of integrating infinite terms, Bull. Amer. Math. Soc. 76 (1970), 605-608. MR 269635
- 15.
- B. M. Trager, On the integration of algebraic functions, Ph.D. thesis, MIT, Cambridge, MA, 1985.
- 16.
- H. S. Wilf, 54 computer-generated proofs of binomial coefficient identities (to appear).
- 17.
- H. S. Wilf and D. Zeilberger, Rational functions certify combinatorial identities, J. Amer. Math. Soc. 3 (1990), 147-158. MR 1007910
- 18.
- J. Wimp and D. Zeilberger, Resurrecting the asymptotics of linear recurrences, J. Math. Anal. Appl. 111 (1985), 162-177. MR 808671
- 19.
- D. Zeilberger, A holonomic systems approach to special function identities, J. Comp. Appl. Math, (to appear). MR 1090884
- 20.
- D. Zeilberger, The method of creative telescoping, J. Symbolic Computation (to appear). MR 1103727
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1985):
05A19
Retrieve articles in all Journals with MSC
(1985):
05A19
Additional Information:
DOI:
10.1090/S0273-0979-1990-15904-X
PII:
S 0273-0979(1990)15904-X
|