Skip to main content
Log in

On a continued fraction of order 12

  • Published:
Ukrainian Mathematical Journal Aims and scope

We present some new relations between a continued fraction U(q) of order 12 (established by M. S. M. Naika et al.) and U(q n) for n = 7, 9, 11, 13:

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. D. Baruah, “Modular equations for Ramanujan’s cubic continued fraction,” J. Math. Anal. Appl., 268, 244–255 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  2. N. D. Baruah and R. Barman, “Certain Theta-function identities and Ramanujan’s modular equations of degree 3,” Indian J. Math., 48, No. 1, 113–133 (2006).

    MathSciNet  MATH  Google Scholar 

  3. B. C. Berndt, Ramanujan Notebooks. Pt. III, Springer, New York (1991).

    MATH  Google Scholar 

  4. B. C. Berndt, Ramanujan Notebooks. Pt. V, Springer, New York (1998).

    MATH  Google Scholar 

  5. H. H. Chan, “On Ramanujan’s cubic continued fraction,” Acta Arithm., 73, No. 4, 343–355 (1995).

    Google Scholar 

  6. H. H. Chan and S. S. Huang, “On the Ramanujan–Göllnitz–Gordan continued fraction,” Ramanujan J., 1., 75–90 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Cho, J. K. Koo, and Y. K. Park, “Arithmetic of the Ramanujan–Göllnitz–Gordan continued fraction,” J. Number Theory, 4, No. 129, 922–947 (2009).

    Article  MathSciNet  Google Scholar 

  8. H. Göllnitz, “Partition mit Differenzebedingungen,” J. Reine Angew. Math., 25, 154–190 (1967).

    Article  Google Scholar 

  9. B. Gordon, “Some continued fractions of the Rogers–Ramanujan type,” Duke Math. J., 32, 741–748 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  10. G. H. Hardy, Ramanujan, Chelsea, New York (1978).

    Google Scholar 

  11. M. S. M. Naika, B. N. Dharmendra, and K. Shivashankra, “A continued fraction of order twelve,” Centr. Eur. J. Math., DOI, 10.2478/s11533-008-0031-y.

  12. S. Ramanujan, Notebooks, Tata Inst. Fundam. Research, Bombay (1957).

  13. S. Ramanujan, The “Lost” Notebook and Other Unpublished Papers, Narosa, New Delhi (1988).

    MATH  Google Scholar 

  14. L. J. Rogers, “On a type of modular relation,” Proc. London Math. Soc., 19, 387–397 (1920).

    Article  Google Scholar 

  15. K. R. Vasuki and P. S. Guruprasad, “On certain new modular relations for the Rogers–Ramanujan type functions of order twelve,” Proc. Jangjeon Math. Soc. (to appear).

  16. K. R. Vasuki, G. Sharath, and K. R. Rajanna, “Two modular equations for squares of the cubic functions with applications,” Note Math. (to appear).

  17. K. R. Vasuki and B. R. Srivatsa Kumar, “Certain identities for Ramanujan–Göllnitz–Gordan continued fraction,” J. Comput. Appl. Math., 187, 87–95 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  18. K. R. Vasuki and B. R. Srivatsa Kumar, Two Identities for Ramanujan’s Cubic Continued Fraction, Preprint.

  19. K. R. Vasuki and S. R. Swamy, “A new identity for the Rogers–Ramanujan continued fraction,” J. Appl. Math. Anal. Appl., 2, No. 1, 71–83 (2006).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 12, pp. 1609–1619, December, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vasuki, K.R., Kahtan, A.A.A., Sharath, G. et al. On a continued fraction of order 12. Ukr Math J 62, 1866–1878 (2011). https://doi.org/10.1007/s11253-011-0476-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-011-0476-1

Keywords

Navigation