Download PDF - Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functionsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions

Authors 1

Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801, U.S.A.

Bibliography

  1. G. E. Andrews, B. C. Berndt, L. Jacobsen and R. L. Lamphere, The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks, Mem. Amer. Math. Soc. 477 (1992).
  2. B. C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991.
  3. B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994.
  4. B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1997.
  5. B. C. Berndt and H. H. Chan, Ramanujan's explicit values for the classical theta-function, Mathematika 42 (1995), 278-294.
  6. B. C. Berndt and H. H. Chan, Some values for the Rogers-Ramanujan continued fraction, Canad. J. Math. 47 (1995), 897-914.
  7. B. C. Berndt, H. H. Chan and L.-C. Zhang, Explicit evaluations of the Rogers-Ramanujan continued fraction, J. Reine Angew. Math. 480 (1996), 141-159.
  8. H. H. Chan, On Ramanujan's cubic continued fraction, Acta Arith. 73 (1995), 343-355.
  9. S.-Y. Kang, Some theorems on the Rogers-Ramanujan continued fraction and associated theta functions in Ramanujan's lost notebook, Ramanujan J. 3 (1999), 91-111.
  10. K. G. Ramanathan, On Ramanujan's continued fraction, Acta Arith. 43 (1984), 209-226.
  11. K. G. Ramanathan, On the Rogers-Ramanujan continued fraction, Proc. Indian Acad. Sci. Math. Sci. 93 (1984), 67-77.
  12. K. G. Ramanathan, Ramanujan's continued fraction, Indian J. Pure Appl. Math. 16 (1985), 695-724.
  13. K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89.
  14. K. G. Ramanathan, On some theorems stated by Ramanujan, in: Number Theory and Related Topics, Tata Inst. Fund. Res. Stud. Math. 12, Oxford Univ. Press, Bombay, 1989, 151-160.
  15. S. Ramanujan, Notebooks (2 volumes), Tata Inst. Fund. Res., Bombay, 1957.
  16. S. Ramanujan, Collected Papers, Chelsea, New York, 1962.
  17. S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford) 45 (1914), 350-372.
  18. S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.
  19. L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318-343.
  20. G. N. Watson, Theorems stated by Ramanujan ( VII): Theorems on continued fractions, J. London Math. Soc. 4 (1929), 39-48.
  21. G. N. Watson, Theorems stated by Ramanujan (IX): Two continued fractions, J. London Math. Soc. 4 (1929), 231-237.
  22. H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961.
Acta Arithmetica
1999/90/1
Export to PBN, Opens in new tab
Pages:
49-68
Main language of publication
English
Received
1998-06-19
Accepted
1998-12-08
Published
1999
Exact and natural sciences