Bijections are given which prove
the following theorems: the q-binomial theorem, Heine’s 2Φ1 transformation, the
q-analogues of Gauss’, Kummer’s, and Saalschütz’s theorems, the very well poised
4Φ3 and 6Φ5 evaluations, and Watson’s transformation of an 8Φ7 to a 4Φ3. The
proofs hold for all values of the parameters. Bijective proofs of the terminating cases
follow from the general case. A bijective version of limiting cases of these series is also
given. The technique is to mimic the classical proofs, based upon a bijective proof of
the q-binomial theorem and sign-reversing involutions which cancel infinite
products.
