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.Comment: 25 pages, in Sec. 3 Table 1 is added, discussion is added at the end
of Sec. 5, minor stylistic changes, typos eliminated. To appear in
Inventiones Mathematica