Abstract :
We show that q-hypergeometric identities k F n, k.s1 can be proved by
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
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
‘‘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’’
checking that its first 2358 cases i.e., values of n. are correct, by direct computa -
tion.
