Ramanujan and the regular continued fraction expansion of real numbers

In some recent papers, the authors considered regular continued fractions of the form \[ \bigg[a_{0};\underbrace{a,\ldots, a}_{m}, \underbrace{a^{2},\ldots, a^{2}}_{m}, \underbrace{a^{3},\ldots, a^{3}}_{m}, \ldots \bigg], \] where -continued fractions investigated by Ramanujan to derive the limits of other infinite families of regular continued fractions.