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

Soon-Yi Kang

Acta Arithmetica (1999)

  • Volume: 90, Issue: 1, page 49-68
  • ISSN: 0065-1036

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Soon-Yi Kang. "Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions." Acta Arithmetica 90.1 (1999): 49-68. <http://eudml.org/doc/207314>.

@article{Soon1999,
author = {Soon-Yi Kang},
journal = {Acta Arithmetica},
keywords = {Rogers-Ramanujan continued fraction; modular equations; theta function; Ramanujan's lost notebook},
language = {eng},
number = {1},
pages = {49-68},
title = {Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions},
url = {http://eudml.org/doc/207314},
volume = {90},
year = {1999},
}

TY - JOUR
AU - Soon-Yi Kang
TI - Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions
JO - Acta Arithmetica
PY - 1999
VL - 90
IS - 1
SP - 49
EP - 68
LA - eng
KW - Rogers-Ramanujan continued fraction; modular equations; theta function; Ramanujan's lost notebook
UR - http://eudml.org/doc/207314
ER -

References

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  1. [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). Zbl0758.40001
  2. [2] B. C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991. Zbl0733.11001
  3. [3] B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994. Zbl0785.11001
  4. [4] B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1997. 
  5. [5] B. C. Berndt and H. H. Chan, Ramanujan's explicit values for the classical theta-function, Mathematika 42 (1995), 278-294. Zbl0862.33016
  6. [6] B. C. Berndt and H. H. Chan, Some values for the Rogers-Ramanujan continued fraction, Canad. J. Math. 47 (1995), 897-914. Zbl0838.33011
  7. [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. Zbl0862.33017
  8. [8] H. H. Chan, On Ramanujan's cubic continued fraction, Acta Arith. 73 (1995), 343-355. Zbl0834.11030
  9. [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. Zbl0930.11025
  10. [10] K. G. Ramanathan, On Ramanujan's continued fraction, Acta Arith. 43 (1984), 209-226. Zbl0535.10007
  11. [11] K. G. Ramanathan, On the Rogers-Ramanujan continued fraction, Proc. Indian Acad. Sci. Math. Sci. 93 (1984), 67-77. Zbl0565.10009
  12. [12] K. G. Ramanathan, Ramanujan's continued fraction, Indian J. Pure Appl. Math. 16 (1985), 695-724. Zbl0573.10001
  13. [13] K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89. Zbl0682.12002
  14. [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. Zbl0746.11009
  15. [15] S. Ramanujan, Notebooks (2 volumes), Tata Inst. Fund. Res., Bombay, 1957. Zbl0138.24201
  16. [16] S. Ramanujan, Collected Papers, Chelsea, New York, 1962. 
  17. [17] S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford) 45 (1914), 350-372. Zbl45.1249.01
  18. [18] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. Zbl0639.01023
  19. [19] L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318-343. 
  20. [20] G. N. Watson, Theorems stated by Ramanujan ( VII): Theorems on continued fractions, J. London Math. Soc. 4 (1929), 39-48. Zbl55.0273.01
  21. [21] G. N. Watson, Theorems stated by Ramanujan (IX): Two continued fractions, J. London Math. Soc. 4 (1929), 231-237. Zbl55.0274.01
  22. [22] H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961. 

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