2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59510Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic ComputationsCombinatoricsNumber TheoryQuantum Algebra05a15, 05a19, 11p81, 11p82, 11p83text