A NEW FOUR PARAMETER q−SERIES IDENTITY AND ITS PARTITION IMPLICATIONS

We prove a new four parameter q-hypergeometric series identity from which the three parameter identity for the Göllnitz theorem due to Alladi, Andrews, and Gordon follows as a special case by setting one of the parameters equal to 0. The new identity is equivalent to a four parameter partition theorem which extends the deep theorem of Göllnitz and thereby settles a problem raised by Andrews thirty years ago. Some consequences including a quadruple product extension of Jacobi’s triple product identity, and prospects of future research are briefly discussed.