单词 | Generalized Hypergeometric Function | ||||||||||||||||||||||||||||||||||||||||||||||||||
释义 | Generalized Hypergeometric FunctionThe generalized hypergeometric function is given by a Hypergeometric Series, i.e., a series for which the ratio of successive terms can be written
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The generalized hypergeometric function
A generalized hypergeometric equation is termed ``well posed'' if
Gosper (1978) discovered a slew of unusual hypergeometric function identities, many of which were subsequently proven by Gesseland Stanton (1982). An important generalization of Gosper's technique, called Zeilberger's Algorithm, in turn led tothe powerful machinery of the Wilf-Zeilberger Pair (Zeilberger 1990). Special hypergeometric identities include Gauss's Hypergeometric Theorem
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![]() ![]() ![]() ![]() ![]() ![]() Gessel (1994) found a slew of new identities using Wilf-Zeilberger Pairs, including the following:
Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, 1935. Dwork, B. Generalized Hypergeometric Functions. Oxford, England: Clarendon Press, 1990. Exton, H. Multiple Hypergeometric Functions and Applications. New York: Wiley, 1976. Gessel, I. ``Finding Identities with the WZ Method.'' Theoret. Comput. Sci. To appear. Gessel, I. and Stanton, D. ``Strange Evaluations of Hypergeometric Series.'' SIAM J. Math. Anal. 13, 295-308, 1982. Gosper, R. W. ``Decision Procedures for Indefinite Hypergeometric Summation.'' Proc. Nat. Acad. Sci. USA 75, 40-42, 1978. Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, 1996. Saxena, R. K. and Mathai, A. M. Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences. New York: Springer-Verlag, 1973. Slater, L. J. Generalized Hypergeometric Functions. Cambridge, England: Cambridge University Press, 1966. Zeilberger, D. ``A Fast Algorithm for Proving Terminating Hypergeometric Series Identities.'' Discrete Math. 80, 207-211, 1990. |
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