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)
     

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


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google