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

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