11/24/2016, 12:53 PM

Let us invastigate the composition and its iterated function. We know the followings:

(f o g) o g^-1 = f

f^-1 o (f o g) = g

☉ f ☥^N = f o f o ... o f (N times), where ☉ is called steinix and ☥ is called ankh.

☉ f ☥^N o ☉ f ☥^M = ☉ f ☥^(N+M)

☉(☉ f ☥^N)☥^M = ☉ f ☥^(N*M)

f o ☉ f ☥^N = ☉ f ☥^N o f = ☉ f ☥^(N+1)

...

etc.

The question is that what the inverses of the ☉ f(x) ☥^N, steinix-ankh formula is?

According to the previous rules, I can find one of the inverses which is the next:

☉(☉ f ☥^N)☥^(1÷N) = f

But I am interested in that what the other inverse is which would give me N.

So ☉ f ☥^N {something operator}(f) = N, what is it? (It might be called steinix-logarithm.)

Any thoughts?

(f o g) o g^-1 = f

f^-1 o (f o g) = g

☉ f ☥^N = f o f o ... o f (N times), where ☉ is called steinix and ☥ is called ankh.

☉ f ☥^N o ☉ f ☥^M = ☉ f ☥^(N+M)

☉(☉ f ☥^N)☥^M = ☉ f ☥^(N*M)

f o ☉ f ☥^N = ☉ f ☥^N o f = ☉ f ☥^(N+1)

...

etc.

The question is that what the inverses of the ☉ f(x) ☥^N, steinix-ankh formula is?

According to the previous rules, I can find one of the inverses which is the next:

☉(☉ f ☥^N)☥^(1÷N) = f

But I am interested in that what the other inverse is which would give me N.

So ☉ f ☥^N {something operator}(f) = N, what is it? (It might be called steinix-logarithm.)

Any thoughts?

Xorter Unizo