单词 | Gosper's Algorithm | ||||||||
释义 | Gosper's AlgorithmAn Algorithm for finding closed form Hypergeometric Identities. The algorithm treatssums whose successive terms have ratios which are Rational Functions. Not only does it decideconclusively whether there exists a hypergeometric sequence
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Petkovsek et al. (1996) describe the algorithm as ``one of the landmarks in the history of computerization of the problem ofclosed form summation.'' Gosper's algorithm is vital in the operation of Zeilberger's Algorithm and the machinery ofWilf-Zeilberger Pairs. See also Hypergeometric Identity, Sister Celine's Method, Wilf-Zeilberger Pair, Zeilberger's Algorithm
Gessel, I. and Stanton, D. ``Strange Evaluations of Hypergeometric Series.'' SIAM J. Math. Anal. 13, 295-308, 1982. Gosper, R. W. ``Decision Procedure for Indefinite Hypergeometric Summation.'' Proc. Nat. Acad. Sci. USA 75, 40-42, 1978. Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994. Lafron, J. C. ``Summation in Finite Terms.'' In Computer Algebra Symbolic and Algebraic Computation, 2nd ed. (Ed. B. Buchberger, G. E. Collins, and R. Loos). New York: Springer-Verlag, 1983. Paule, P. and Schorn, M. ``A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities.'' J. Symb. Comput. 20, 673-698, 1995. Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. ``Gosper's Algorithm.'' Ch. 5 in A=B. Wellesley, MA: A. K. Peters, pp. 73-99, 1996. Zeilberger, D. ``The Method of Creative Telescoping.'' J. Symb. Comput. 11, 195-204, 1991. |
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