Table of Contents
ISRN Computational Mathematics
Volume 2012, Article ID 169050, 14 pages
http://dx.doi.org/10.5402/2012/169050
Research Article

A Parameter for Ramanujan's Function χ(q): Its Explicit Values and Applications

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

Received 3 May 2012; Accepted 28 June 2012

Academic Editors: L. Hajdu, L. S. Heath, and H. J. Ruskin

Copyright © 2012 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, Notebooks, vol. 1-2, Tata Institute of Fundamental Research, Bombay, India, 1957.
  2. B. C. Berndt, Ramanujan's Notebooks. Part III, Springer, New York, NY, USA, 1991. View at Publisher Β· View at Google Scholar
  3. S. Ramanujan, β€œModular equations and approximations to π,” Quarterly Journal of Mathematics, vol. 45, pp. 350–372, 1914. View at Google Scholar
  4. H. Weber, Lehrburg Der Algebra II,, Chelsea, New York, NY, USA, 1961.
  5. B. C. Berndt, Ramanujan's Notebooks. Part V, Springer, New York, NY, USA, 1998. View at Publisher Β· View at Google Scholar
  6. N. D. Baruah, β€œOn some class invariants of Ramanujan,” The Journal of the Indian Mathematical Society, vol. 68, no. 1–4, pp. 113–131, 2001. View at Google Scholar
  7. B. C. Berndt and H. H. Chan, β€œSome values for the Rogers-Ramanujan continued fraction,” Canadian Journal of Mathematics, vol. 47, no. 5, pp. 897–914, 1995. View at Publisher Β· View at Google Scholar
  8. B. C. Berndt, H. H. Chan, S. Y. Kang, and L. C. Zhang, β€œA 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 Google Scholar Β· View at Scopus
  9. B. C. Berndt, H. H. Chan, and L.-C. Zhang, β€œRamanujan's class invariants with applications to the values of q-continued fractions and theta functions,” in Special Functions, q-Series and Related Topics, M. Ismail, D. Masson, and M. Rahman, Eds., vol. 14 of Fields Institute Communications Series, pp. 37–53, American Mathematical Society, Providence, RI, USA, 1997. View at Google Scholar
  10. B. C. Berndt, H. H. Chan, and L. C. Zhang, β€œRamanujan's class invariants and cubic continued fraction,” Acta Arithmetica, vol. 73, no. 1, pp. 67–85, 1995. View at Google Scholar
  11. B. C. Berndt, H. H. Chan, and L. C. Zhang, β€œRamanujan's remarkable product of theta-functions,” Proceedings of the Edinburgh Mathematical Society, vol. 40, no. 3, pp. 583–612, 1997. View at Google Scholar Β· View at Scopus
  12. N. Saikia, β€œRamanujan's modular equations and Weber-Ramanujan's class invariants Gn and gn,” Bulletin of Mathematical Sciences, vol. 2, no. 1, pp. 205–223, 2012. View at Publisher Β· View at Google Scholar
  13. J. Yi, Construction and application of modular equation [Ph.D. thesis], University of Illionis, 2001.
  14. J. Yi, β€œTheta-function identities and the explicity formulas for theta-function and their applications,” Journal of Mathematical Analysis and Applications, vol. 292, no. 2, pp. 381–400, 2004. View at Publisher Β· View at Google Scholar Β· View at Scopus
  15. K. R. Vasuki and T. G. Sreeramamurthy, β€œCertain new Ramanujan's Schläfli-type mixed modular equations,” Journal of Mathematical Analysis and Applications, vol. 309, no. 1, pp. 238–255, 2005. View at Publisher Β· View at Google Scholar Β· View at Scopus
  16. N. D. Baruah, β€œOn some of Ramanujan's Schläfli-type 'mixed' modular equations,” Journal of Number Theory, vol. 100, no. 2, pp. 270–294, 2003. View at Publisher Β· View at Google Scholar Β· View at Scopus