2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63533In a recent paper by the authors, a bounded version of Goellnitz's (big) partition theorem was established. Here we show among other things how this theorem leads to nontrivial new polynomial analogues of certain fundamental identities of Jacobi and Lebesgue. We also derive a two parameter extension of Jacobi's famous triple product identity.19 pagesCombinatoricsNumber TheoryQuantum Algebra05A19, 05A30, 11P82, 33D15text