In this paper we show that various continued fr
actions for the quotient of general Ramanujan functions
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306485&_mathId=si1.gif&_user=111111111&_pii=S0022247X16306485&_rdoc=1&_issn=0022247X&md5=b88ba68cb3274317b37d98e9081e0393" title="Click to view the MathML source">G(aq,b,λq)/G(a,b,λ)class="mathContainer hidden">class="mathCode"> may
be derived from e
ach other via Bauer–Muir transformations. The separate convergence of numerators and denominators play a key part in showing that the continued fr
actions and their Bauer–Muir transformations converge to the same limit. We also show that these continued fr
actions may
be derived from either Heine's continued fr
action for a ratio of
class="mathmlsrc">class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306485&_mathId=si2.gif&_user=111111111&_pii=S0022247X16306485&_rdoc=1&_issn=0022247X&md5=972701359f6b7d8d3ff947b0b550ecd4">
class="imgLazyJSB inlineImage" height="15" width="25" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16306485-si2.gif">class="mathContainer hidden">class="mathCode"> functions, or other similar continued fr
action expansions of ratios of
class="mathmlsrc">class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306485&_mathId=si2.gif&_user=111111111&_pii=S0022247X16306485&_rdoc=1&_issn=0022247X&md5=972701359f6b7d8d3ff947b0b550ecd4">
class="imgLazyJSB inlineImage" height="15" width="25" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16306485-si2.gif">class="mathContainer hidden">class="mathCode"> functions. Further, by employing essentially the same methods, a new continued fr
action for
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306485&_mathId=si1.gif&_user=111111111&_pii=S0022247X16306485&_rdoc=1&_issn=0022247X&md5=b88ba68cb3274317b37d98e9081e0393" title="Click to view the MathML source">G(aq,b,λq)/G(a,b,λ)class="mathContainer hidden">class="mathCode"> is derived. Finally we derive a num
ber of new versions of some
beautiful continued fr
action expansions of Ramanujan for certain combinations of infinite products, with the following
being an example:
class="formula" id="fm0880">