An identity for the infinite sum ${\sum }_{n=0}^{\mathrm{\infty }}\frac{1}{(n!{)}^3}$

In this short note, we give an identity for the $\alpha$ function $$\alpha (x,s)=\sum _{n=0}^{\mathrm{\infty }}\frac{x^n}{(n!{)}^s}$$ where $s\in \mathbb{N}$, $x\in \mathbb{R}$, in the case $s=3$.