What is a 2-fraction?

I am working with a 4-term recurrence relation coming from the application of the Frobenius method on a ODE, in particular I am studying the convergence of the resulting series. Trying to find out a method to find conditions that impose convergence on the series I came across this paper which uses 2-fractions. They seem to be a generalization of continued fractions, but I cannot find anything on the internet on this subject.

What is a 2-fraction? And how do I deal with it?