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On the Rogers-Ramanujan continued fraction

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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.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Bombay, India

    K. G. Ramanathan

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  1. K. G. Ramanathan
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Ramanathan, K.G. On the Rogers-Ramanujan continued fraction. Proc. Indian Acad. Sci. (Math. Sci.) 93, 67–77 (1984). https://doi.org/10.1007/BF02840651

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