User blog:IIEnDeRwITHeRII/Omega Function

The Omega Function $$Omega$$ is a function that signifies exponential factorialization.

---Definition---

$$Omega$$n = $$n^n-1^n-2^...^2^1$$.

$$f(n)Omega$$n = $$n^f(n-1)^f(n-2)^....^f(1)$$.

---Instantaneous Rate Of Growth---

The instantaneous rate of growth of the omega function can be found by taking the derivative of $$Omega$$n.

We know that $$Omega$$n = $$n^n-1^...^1$$.

Using the power rule of derivatives, $$d/dxOmega$$n = Omega n-1[n^(Omega n-1)-1].

---Origin---

The Omega Function was coined by Googology wikia user IIEnDeRwITHeRII in 2018, in the early days of May.