In this paper we study the special cases $\{_vM_m(s;m+n,z)^\infty_{n=2}$ and $\{_vM_m(s;a,n)\}^\infty_{n=1}$, where $_vM_m(s;a,z)$ is the function defined in [8]. Also, we give connections between $_vM_m(s;a,z)$ function and figured numbers, Stirling numbers of the first kind and Riemann Zeta function.