My function $M(x)$ is defined as $$M(x)=1+\cfrac{x^0}{1+\cfrac{x^1}{1+\cfrac{x^2}{1+\cfrac{x^3}{1+\cfrac{x^4}{1+\cfrac{x^5}{1+\cfrac{x^{6}}{1+\cfrac{x^{7}}{1+\cfrac{x^{8}}{1+\cfrac{x^9}{1+\cfrac{x^{10}}{1+\ddots}}}}}}}}}}}$$
I understand the Rogers-Ramanujan Continued Fraction $R(a,q)$ is very similar but it is slightly different. I would like to know what $M(2)$ is, but I learned that any value $|q|>1$ starts to split and become two different values. What are the decimal approximations of $M(2)$ for both $n$=even and $n$=odd and what are their exact values?
This is my first question on this site so if it's janky or similar to an answer already I'm sorry.