• K G Ramanathan

      Articles written in Proceedings – Mathematical Sciences

    • On the Rogers-Ramanujan continued fraction

      K G Ramanathan

      More Details Abstract Fulltext PDF

      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.

    • Hypergeometric series and continued fractions

      K G Ramanathan

      More Details Abstract Fulltext PDF

      Ramanujan’s results on continued fractions are simple consequences of three-term relations between hypergeometric series. Theirq-analogues lead to many of the continued fractions given in the ‘Lost’ notebook in particular the famous one considered by Andrews and others.

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