  We prove a new four parameter q-hypergeometric series identity from which the
three parameter key identity for the Goellnitz 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 Goellnitz 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.
