On the Rogers-Ramanujan continued fraction

  • K. G. Ramanathan


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.


Continued fractions Kronecker limit formula Dirichlet series 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Borevich Z I and Shafarevich I R 1966Number theory (New York: Academic Press)zbMATHGoogle Scholar
  2. [2]
    Fricke R and Klein F 1892 Vorlesungen über die theorie der elliptischen Modulfunktionen Bd2Google Scholar
  3. [3]
    Ramanathan K G 1984Acta Arith. 44 209MathSciNetGoogle Scholar
  4. [4]
    Ramanathan K G 1980Proc. Indian Acad. Sci (Math. Sci.) 89 133zbMATHMathSciNetGoogle Scholar
  5. [5]
    Ramanujan S 1987Note books, I and II printed facsimile (Bombay: TIFR)Google Scholar
  6. [6]
    Ramanujan SLost Note book (unpublished manuscripts in the library, Trinity College, Cambridge, England)Google Scholar
  7. [7]
    Rogers L J 1894Proc. London Math. Soc. 25 318CrossRefGoogle Scholar
  8. [8]
    Siegel C L 1980Advanced analytic number theory. Studies in mathematics (Bombay: TIFR)Google Scholar
  9. [9]
    Watson G N 1929J. London Math. Soc. 4 39Google Scholar
  10. [10]
    Whittaker E T and Watson G N1946A course of modern analysis (Cambridge University Press) 4th ednGoogle Scholar
  11. [11]
    Weber H 1908Lehrb. Algebra III BraunschweigGoogle Scholar

Copyright information

© Indian Academy of Sciences 1984

Authors and Affiliations

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

Personalised recommendations