On the Rogers-Ramanujan continued fraction

  • K. G. Ramanathan
Article

DOI: 10.1007/BF02840651

Cite this article as:
Ramanathan, K.G. Proc. Indian Acad. Sci. (Math. Sci.) (1984) 93: 67. doi:10.1007/BF02840651

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 fractionsKronecker limit formulaDirichlet series

Copyright information

© Indian Academy of Sciences 1984

Authors and Affiliations

  • K. G. Ramanathan
    • 1
  1. 1.School of MathematicsTata Institute of Fundamental ResearchBombayIndia