Continued fractions for some transcendental numbers
Continued fractions for some transcendental numbers
We consider series of the form $$\begin{aligned} \frac{p}{q} +\sum _{j=2}^\infty \frac{1}{x_j}, \end{aligned}$$ where $$x_1=q$$ and the integer sequence $$(x_n)$$ satisfies a certain non-autonomous recurrence of second order, which entails that $$x_n|x_{n+1}$$ for $$n\ge 1$$ . It is shown that the terms of the sequence, and multiples of the ratios of …