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On the Rogers-Ramanujan continued fraction
Authors:K G Ramanathan
Institution:(1) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005 Bombay, India
Abstract:In the “Lost” note book, Ramanujan had stated a large number of results regarding evaluation of his continued fraction 
$$R(\tau ) = \frac{{exp2\pi i\tau /}}{{1 + }}\frac{{5exp(2\pi i\tau )}}{{1 + }}\frac{{exp(4\pi i\tau )}}{{1 + }}...$$
for certain values of τ. It is shown that all these results and many more have their source in the Kronecker limit formula.
Keywords:Continued fractions  Kronecker limit formula  Dirichlet series
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