Finding the Solution for y = 1 - n/(y^n) in Terms of Using Special Funct

Hello,

I am currently researching iterative functional differential equations and have encountered a challenging problem. Specifically, I am trying to solve the equation:

$$ y = 1 - \frac{n}{y^n} $$

for \( y \) in terms of \( n \). I am open to using any special functions, such as the Lambert W function, or even defining a new function if necessary.

To give more context, this equation arises from my studies on the behavior of certain iterative processes, and finding an explicit form for \( y \) would greatly aid my research.

Any insights, approaches, or references to similar problems would be highly appreciated.

Thank you!

Tags:
- iterative functions
- differential equations
- special functions
- Lambert W function
- mathematical research