In this paper we show that various continued fr
ac tions 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">G ( a q , b , λ q ) / G ( a , b , λ ) may be derived from e
ac h other via Bauer–Muir transformations. The separate convergence of numerators and denominators play a key part in showing that the continued fr
ac tions and their Bauer–Muir transformations converge to the same limit. We also show that these continued fr
ac tions may be derived from either Heine's continued fr
ac tion 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">ϕ 1 2 functions, or other similar continued fr
ac tion 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">ϕ 1 2 functions. Further, by employing essentially the same methods, a new continued fr
ac tion 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">G ( a q , b , λ q ) / G ( a , b , λ ) is derived. Finally we derive a number of new versions of some beautiful continued fr
ac tion expansions of Ramanujan for certain combinations of infinite products, with the following being an example:
class="formula" id="fm0880">