• On the Rogers-Ramanujan continued fraction

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/093/02-03/0067-0077

    • Keywords

       

      Continued fractions; Kronecker limit formula; Dirichlet series

    • 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.

    • Author Affiliations

       

      K G Ramanathan1

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

       
  • Proceedings – Mathematical Sciences | News

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