A maple program for proving hypergeometric identities

ABSTRACT

In [Z1](see also [Z2],[WZ],[S],[Ci]) I gave an algorithm for proving any terminating definite hypergeometric identity, and more generally, for finding the linear recurrence satisfied by any definite hypergeometric sum[EQUATION]

REFERENCES

• 1: {Ba} Bailey, W. N., "Generalized Hypergeometric Series", Cambridge Math. Tracts <b>32</b>, Cambridge University Press, London, 1935. (Reprinted: Hafner, New York,. 1964.)
• 2: Gregory J. Chaitin, Algorithmic information theory, Cambridge University Press, New York, NY, 1987
• 3: {Ci} Cipra, B., <i>How the Grinch Stole Mathematics</i>, Science <b>245</b> (1989) (11 Aug 1989), p. 595.
• 4: {Go} Gosper, R. W., Jr., <i>Decision Procedure of Indefinite Summation</i>, Proc. Natl. Acad. Sci. USA <b>75</b>, 40--42, 1978.
• 5: {S} Sangalli, A., <i>The automatic proofing machine</i>, New Scientist No. 1687 (21 Oct 1989), p. 37.
• 6: {WZ} Wilf, H. S., and Zeilberger, D., <i>Towards computerized proofs of identities</i>, Bulletin of the Amer. Math. Soc., to appear.
• 7: {Wi} Wilson, J. A., <i>Some hypergeometric orthogonal polynomials</i>, SIAM J. Math. Anal. <b>11</b>(1980), 690--701.
• 8: Doron Zeilberger, The method of creative telescoping, Journal of Symbolic Computation, v.11 n.3, p.195-204, March 1991 [doi>10.1016/S0747-7171(08)80044-2]
• 9: D. Zeiberger, A fast algorithm for proving terminating hypergeometric identities, Discrete Mathematics, v.80 n.2, p.207-211, March 1990 [doi>10.1016/0012-365X(90)90120-7]

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems

          Nouns: Maple

Additional Classification:
  G. Mathematics of Computing
  G.2 DISCRETE MATHEMATICS
      G.2.1 Combinatorics
          Subjects: Generating functions

General Terms:
Algorithms, Theory, Verification