On the Recurrence Relation Between Mock Theta Function and Various Partition Functions

In this paper, we present some recurrence relations for partition function $$p_\omega(n)$$ , which is associated with the third order mock theta function $$\omega(q)$$ . We will also find the connection of partition function $$p_\omega(n)$$ with the restricted partition function $$p_{ld}(n)$$ , where $$p_{ld}(n)$$ denote the number of partitions into distinct parts with $$l$$ copies.