let $$f(x)= \sum_{n=1}^{\infty}a_n x^n$$ where $a_n\in \{0,1\}$, and the $f(x)$ has a natural boundary. By the way, $$f(x)= \sum_{n=1}^{\infty}a_n x^n$$ is rational function or transcendental one on $C$。

Is $f(x)$ at $\frac{1}{10}$ transcendental? Or is value of such a transcendental function of power series  at  $\frac{1}{10}$ a transcendental number?