Take the 2-minute tour ×   How can a power series be found given
the continued fraction $f(x)$?  I'm trying to find $f(x) =1+a_1x
+\dfrac{a_2x^2}{2!}+\dfrac{a_3x^3}{3!}+\dfrac{a_4x^4}{4!}+\cdots
$  I tried some ways to define $f(x)$ but I could not find the
general patern. It goes to complex patern after $n=3$ in my
approach. I think that I need another approach to problem.
$$\begin{align} &f_1(x)=\frac{1}{1+x}=1-x+x^2-x^3+\ldots\\
&f_2(x)=\frac{1}{1+\frac{x}{1+x^2}}=\frac{1+x^2}{1+x+x^2}\\ &f_3
(x)=\frac{1}{1+\frac{x}{1+\frac{x^2}{1+x^3}}}=\frac{1+x^2+x^3}{1
+x+x^2+x^3+x^4}\\ &\lim_{n\to \infty} {f_n(x)}=f(x)
\end{align}$$  Could you please give me hand on how to find the
patern of this function?  share|improve this question add
comment  1 Answer  up vote 5 down vote accepted  You are looking
for the reciprocal of the classic Rogers-Ramanujan Continued
fraction. A listing of some of the power series coefficients can
be found here: OEIS. You might be able to find more references
there.  share|improve this answer