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On the Rogers-Ramanujan continued fraction
Authors:K. G. Ramanathan
Affiliation:(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 
$$R(tau ) = frac{{exp2pi itau /}}{{1 + }}frac{{5exp(2pi itau )}}{{1 + }}frac{{exp(4pi itau )}}{{1 + }}...$$
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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