By considering a limiting form of the q-Dixon 4φ3 summation, we prove a weighted partition theorem involving odd parts differing by ≥ 4. A two parameter refinement of this theorem is then deduced from a quartic reformulation of Göllnitz’s (Big) theorem due to Alladi, and this leads to a two parameter extension of Jacobi’s triple product identity for theta functions. Finally, refinements of certain modular identities of Alladi connected to the Göllnitz-Gordon series are shown to follow from a limiting form of the q-Dixon 4φ3 summation.
q-Dixon sum q-Dougall Sum weighted partition identities Göllnitz’s (Big) theorem quartic reformulation Jacobi’s triple product GöllnitzGordon identities modular relations
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