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

Acta Arithmetica (1999)

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

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topSoon-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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- [2] B. C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991. Zbl0733.11001
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- [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. Zbl0862.33016
- [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] 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] H. H. Chan, On Ramanujan's cubic continued fraction, Acta Arith. 73 (1995), 343-355. Zbl0834.11030
- [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] K. G. Ramanathan, On Ramanujan's continued fraction, Acta Arith. 43 (1984), 209-226. Zbl0535.10007
- [11] K. G. Ramanathan, On the Rogers-Ramanujan continued fraction, Proc. Indian Acad. Sci. Math. Sci. 93 (1984), 67-77. Zbl0565.10009
- [12] K. G. Ramanathan, Ramanujan's continued fraction, Indian J. Pure Appl. Math. 16 (1985), 695-724. Zbl0573.10001
- [13] K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89. Zbl0682.12002
- [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] S. Ramanujan, Notebooks (2 volumes), Tata Inst. Fund. Res., Bombay, 1957. Zbl0138.24201
- [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. Zbl45.1249.01
- [18] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. Zbl0639.01023
- [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. Zbl55.0273.01
- [21] G. N. Watson, Theorems stated by Ramanujan (IX): Two continued fractions, J. London Math. Soc. 4 (1929), 231-237. Zbl55.0274.01
- [22] H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961.

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