Skip to main content

Two generalizations of Ramanujan's continued fraction identities

Part of the Lecture Notes in Mathematics book series (LNM,volume 1122)

Key words

  • q-continued fractions
  • Rogers-Ramanujan continued fractions

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.E. Andrews, An Introduction to Ramanujan's “lost” notebook, Amer. Math. Monthly, 86 (1979), 89–108.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. G.E. Andrews, Ramanujan's “lost” notebook III-The Rogers-Ramanujan continued fraction, Advances Math. 41 (1981), 186–208.

    CrossRef  MATH  Google Scholar 

  3. S. Bhargava and Chandrashekar Adiga, On some continued fraction identities of Srinivasa Ramanujan, Proc. Amer. Math. Soc. (to appear).

    Google Scholar 

  4. E. Heine, Untersuchungen über die Reihe \(1 + \frac{{(1 - {q^\alpha })(1 - {q^\beta })}}{{(1 - q)(1 - {q^\alpha })}}x + \frac{{(1 - {q^\alpha })(1 - {q^{\alpha + 1}})(1 - {q^\beta })(1 - {q^{\beta + 1}})}}{{(1 - q)(1 - {q^2})(1 - {q^\alpha })(1 - {q^{\alpha + 1}})}}{x^2} + \ldots\) J. Reine. Angew Math. 34 (1847), 285–328.

    CrossRef  MathSciNet  Google Scholar 

  5. M.D. Hirschhora, A continued fraction, Duke Math. J. 41 (1974), 27–33.

    CrossRef  MathSciNet  Google Scholar 

  6. M.D. Hirschhorn, A continued fraction of Ramanujan, J. Aust. Math. Soc. (Series A) 29 (1980) 80–86.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. S. Ramanujan, Notebooks (Vol. I and II), TIFR, Bombay (1957); Springer-Verlag, Berlin-Heidelberg.

    Google Scholar 

  8. S. Ramanujan, Unpublished manuscripts (1920 ?).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to Paul Erdös on his seventieth birthday

Rights and permissions

Reprints and Permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Bhargava, S., Adiga, C. (1985). Two generalizations of Ramanujan's continued fraction identities. In: Alladi, K. (eds) Number Theory. Lecture Notes in Mathematics, vol 1122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075750

Download citation

  • DOI: https://doi.org/10.1007/BFb0075750

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15222-4

  • Online ISBN: 978-3-540-39642-0

  • eBook Packages: Springer Book Archive