Table of Contents
ISRN Computational Mathematics
Volume 2013, Article ID 435261, 8 pages
Research Article

Some New Explicit Values of Parameters and of Quotients of Eta-Function

Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh 791112, India

Received 9 November 2012; Accepted 16 December 2012

Academic Editors: T. Allahviranloo and G. Germano

Copyright © 2013 Nipen Saikia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, India, 1988.
  2. B. C. Berndt, H. H. Chan, S.-Y. Kang, and L.-C. Zhang, “A certain quotient of eta-functions found in Ramanujan's lost notebook,” Pacific Journal of Mathematics, vol. 202, no. 2, pp. 267–304, 2002. View at Publisher · View at Google Scholar
  3. G. E. Andrews and B. C. Berndt, Ramanujan's Lost Notebook. Part II, Springer, New York, NY, USA, 2009.
  4. K. G. Ramanathan, “On some theorems stated by Ramanujan,” in Number Theory and Related Topics (Bombay, 1988), vol. 12, pp. 151–160, Oxford University Press, Bombay, India, 1989. View at Google Scholar
  5. J. Yi, Construction and application of modular equation [Ph.D. thesis], University of Illionis, Chicago, Ill, USA, 2001.
  6. J. Yi, “Some new modular equations and their applications,” Journal of Mathematical Analysis and Applications, vol. 319, no. 2, pp. 531–546, 2006. View at Publisher · View at Google Scholar
  7. N. D. Baruah and N. Saikia, “Some general theorems on the explicit evaluations of Ramanujan's cubic continued fraction,” The Journal of Computational and Applied Mathematics, vol. 160, no. 1-2, pp. 37–51, 2003. View at Google Scholar
  8. N. D. Baruah and N. Saikia, “Some new explicit values of Ramanujan's continued fractions,” Indian Journal of Mathematics, vol. 46, no. 2-3, pp. 197–222, 2004. View at Google Scholar
  9. M. S. M. Naika, M. C. Maheshkumar, and K. S. Bairy, “Certain quotient of eta-function identities,” Advanced Studies in Contemporary Mathematics, vol. 16, no. 1, pp. 121–136, 2008. View at Google Scholar
  10. B. C. Berndt, Ramanujan's Notebooks. V, Springer, New York, NY, USA, 1998. View at Publisher · View at Google Scholar
  11. N. D. Baruah, “On some class invariants of Ramanujan,” The Journal of the Indian Mathematical Society. New Series, vol. 68, no. 1–4, pp. 113–131, 2001. View at Google Scholar
  12. N. Saikia, “Ramanujan's Schläfli-type modular equations and class invariants gn,” Functiones et Approximatio Commentarii Mathematici. In press.
  13. N. Saikia, “Ramanujan's modular equations and Weber-Ramanujan class invariants Gn and gn,” Bulletin of Mathematical Sciences, vol. 2, no. 1, pp. 205–223, 2012. View at Publisher · View at Google Scholar
  14. N. Saikia, “A parameter for Ramanujans function χ(q): its explicit values and applications,” ISRN Computational Mathematics, vol. 2012, Article ID 169050, 14 pages, 2012. View at Publisher · View at Google Scholar
  15. B. C. Berndt, Ramanujan's Notebooks. III, Springer, New York, NY, USA, 1991. View at Publisher · View at Google Scholar