I'm trying to formally define (generalized) continued fraction.
Consider $[i;\sqrt2,i,i]$.
This is not well defined since $i+\frac{1}{i}=0$.
What would be a domain of continued fraction? (As a function)
That is, how do I formally define continued fraction?
EDIT:
I have searched for it, and it's on wikipedia that continued fraction can be defined by using Möbius transformation.
Since I'm familiar with Möbius transformation, I see this definition is perfectly formal. Is this the standard definition? If not, what is the standard definition?