Abstract
Given 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 Göllnitz’s (big) theorem follows if L, M →∞. When L = M, the identity yields a strong refinement of Gölhiitz’s theorem with a bound on the parts given by L. This is the first time a bounded version of Göllnitz’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.KeywordsGöllnitz partition theoremdouble bounded identityq—multinomial coefficientsrecursion relationspolynomial versions of Jacobi’s formulas
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