The Lambert $W$ Function is defined in this Wikipedia entry, while the Hypergeometric Function is defined in this other Wikipedia entry. There exists also a multivariate generalization which solves the following equation $$ e^{-c x}=d \frac{\left(x-a_{0}\right)\left(x-a_{1}\right) \cdots\left(x-a_{n}\right)}{\left(x-b_{0}\right)\left(x-b_{1}\right) \cdots\left(x-b_{m}\right)} $$

as I read from Quora post. This equation has some analogies in Hypergeometric functions as well.

I also would like to know if the Lambert $W$ Function can be written as an inverse of Hypergeometric functions: is it so? Or are there any other kind of relationship about them? Thanks for your answers and references.