Sums over Partitions into Distinct Parts

In this paper, we are going to present sums over partitions. We define a function uₙ(g; q), which can be considered as one generalization of q-Pochhammer symbol. Using this function uₙ(g; q), many results have been proved for sums of partitions into even distinct parts, odd distinct parts, 1 as the only part and v = v as a part.