So I made this Bump Funk, and the first version was basically defined as follows:
(all ordinals in Cantor Normal Form)
If your ordinal is not one of the above, then
Where represents the -th ordinal in the fundamental sequence of .
Let's look at an example:
Pretty basic right? Now we have my Bump Ordinal Collapsing Funk, BOCF or .
And so we have...
In general, for and being a perfect multiple/power of , we have that this is equal to Madore's psi function.
We can then go further that Madore's psi function since
In general, we have
So now we can do neat little things like
And furthermore, since , we can even go further...