  In this paper we show that various continued fractions for the quotient of
general Ramanujan functions $G(aq,b,\l q)/G(a,b,\l)$ may be derived from each
other via Bauer-Muir transformations. The separate convergence of numerators
and denominators play a key part in showing that the continued fractions and
their Bauer-Muir transformations converge to the same limit.
  We also show that these continued fractions may be derived from Heine's
continued fraction for a ratio of $_2\phi_1$ functions and other continued
fractions of a similar type, and by this method derive a new continued fraction
for $G(aq,b,\l q)/G(a,b,\l)$.
  Finally we derive a number of new versions of some beautiful continued
fraction expansions of Ramanujan for certain combinations of infinite products,
with the following being an example: \begin{multline*} \frac{(-a,b;q)_{\infty}
- (a,-b;q)_{\infty}}{(-a,b;q)_{\infty}+ (a,-b;q)_{\infty}} = \frac{(a-b)}{1-a
b} \- \frac{(1-a^2)(1-b^2)q}{1-a b q^2}\\ \- \frac{(a-bq^2)(b-aq^2)q}{1-a b
q^4} %\phantom{sdsadadsaasdda}\\ \- \frac{(1-a^2q^2)(1-b^2q^2)q^3}{1-a b q^6}
\- \frac{(a-bq^4)(b-aq^4)q^3}{1-a b q^8} \- \cds . \end{multline*}

Number Theory