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

Discussion in 'Differential Equations' started by Michael J, Jun 27, 2024.

  1. Michael J

    Michael J

    Jun 27, 2024
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    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!

    - iterative functions
    - differential equations
    - special functions
    - Lambert W function
    - mathematical research
    Michael J, Jun 27, 2024
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