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A Two-Line Algorithm for Provingq-Hypergeometric Identities

✍ Scribed by Lily Yen

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 206 KB
Volume: 213
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5131

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✦ Synopsis

We show that q-hypergeometric identities Ý F n, k s 1 can be proved by k checking that they are correct for only finitely many, N say, values of n. We give a specific a priori formula for N, as a polynomial of degree 24 in the parameters of Ž . F n, k . We see this because of the presence of ''q'', the estimates of N can be made smaller than the general estimates that were found in the author's thesis Ž''Contributions to the Proof Theory of Hypergeometric Identities,'' pp. 1᎐83, . Ph.D. thesis, University of Pennsylvania, Philadelphia, 1993 . As an example of the method we show that the q-Vandermonde identity can be pro¨ed by ''only'' Ž . checking that its first 2358 cases i.e., values of n are correct, by direct computation.

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