Lambert W Function is defined https://en.wikipedia.org/wiki/Lambert_W_function

  Hypergeometric Function is defined https://en.wikipedia.org/wiki/Hypergeometric_function

$e^{-c x}=d \frac{\left(x-a_{0}\right)\left(x-a_{1}\right) \cdots\left(x-a_{n}\right)}{\left(x-b_{0}\right)\left(x-b_{1}\right) \cdots\left(x-b_{m}\right)}$

I read from https://www.quora.com/How-is-the-Lambert-W-function-derived This equation has some analogies in Hypergeometric functions as well.

I also want to ask Lambert W Function can be written inverse of Hypergeometric functions? Or are there any relationship about them? Thanks for your answers and references.

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.

Lambert W Function is defined https://en.wikipedia.org/wiki/Lambert_W_function

Hypergeometric function is defined https://en.wikipedia.org/wiki/Hypergeometric_function

Is there any relationships about these two functions ? ı didn't see any article about it.

I also want to ask Lambert w function can be written inverse of Hypergeometric functions? Why or why not? Thanks for your answers and references.

Lambert W Function is defined https://en.wikipedia.org/wiki/Lambert_W_function

Hypergeometric Function is defined https://en.wikipedia.org/wiki/Hypergeometric_function

$e^{-c x}=d \frac{\left(x-a_{0}\right)\left(x-a_{1}\right) \cdots\left(x-a_{n}\right)}{\left(x-b_{0}\right)\left(x-b_{1}\right) \cdots\left(x-b_{m}\right)}$

I read from https://www.quora.com/How-is-the-Lambert-W-function-derived This equation has some analogies in Hypergeometric functions as well.

I also want to ask Lambert W Function can be written inverse of Hypergeometric functions? Or are there any relationship about them? Thanks for your answers and references.