On mock theta functions of Gordon and McIntosh

A new approach involving the concept of modular Ferrers diagram is employed to interpret the Gordon and McIntosh’s mock theta functions in terms of \({(n+t)}\) $(n+t)$ -color partitions. We then provide the generalized versions of the mock theta functions and their interpretations. We further found some arithmetic properties for two of the mock theta functions \(\beta (q)\) $\beta (q)$ and \(\xi (q)\) $\xi (q)$ .