I'm looking for a number series I can use for gradually rising or falling numbers. The number series should not be linear and should converge to a number at some point.
$\sqrt[N]{N}$ where $N > 3$; $N \in \mathbb{Z}$. (This series gradually falls)
Its inverse is then used for the opposite
I've verified for $N$ for the set $[4,5,\ldots,9]$
Do you know about other options? Other things I should consider?
They don't need to be inverses.
You can use $e^{-kn}$ for a falling series and $1-e^{-kn}$ for rising. Or $\frac 1{1+n}$ for falling and $\frac n{n+1}$ for rising. There are lots of possibilities-better definition is needed.