# On Ramanujan's cubic continued fraction

Acta Arithmetica (1995)

- Volume: 73, Issue: 4, page 343-355
- ISSN: 0065-1036

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topHeng Huat Chan. "On Ramanujan's cubic continued fraction." Acta Arithmetica 73.4 (1995): 343-355. <http://eudml.org/doc/206824>.

@article{HengHuatChan1995,

author = {Heng Huat Chan},

journal = {Acta Arithmetica},

keywords = {algorithm for computing , modular equations; numerical values; reciprocity theorems; Borwein's cubic theta function identity; identities; Ramanujan's cubic continued fraction},

language = {eng},

number = {4},

pages = {343-355},

title = {On Ramanujan's cubic continued fraction},

url = {http://eudml.org/doc/206824},

volume = {73},

year = {1995},

}

TY - JOUR

AU - Heng Huat Chan

TI - On Ramanujan's cubic continued fraction

JO - Acta Arithmetica

PY - 1995

VL - 73

IS - 4

SP - 343

EP - 355

LA - eng

KW - algorithm for computing , modular equations; numerical values; reciprocity theorems; Borwein's cubic theta function identity; identities; Ramanujan's cubic continued fraction

UR - http://eudml.org/doc/206824

ER -

## References

top- [1] G. E. Andrews, B. C. Berndt, L. Jacobsen and R. C. Lamphere, The continued fractions found in the unorganised portions of Ramanujan's notebooks, Mem. Amer. Math. Soc. 477 (1992). Zbl0758.40001
- [2] B. C. Berndt, Ramanujan Notebooks, Part III, Springer, New York, 1991.
- [3] B. C. Berndt, Ramanujan Notebooks, Part IV, Springer, New York, 1994.
- [4] J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, New York, 1987.
- [5] J. M. Borwein and P. B. Borwein, A cubic counterpart of Jacobi's identity and the AGM, Trans. Amer. Math. Soc. 323 (1991), 691-701. Zbl0725.33014
- [6] J. M. Borwein, P. B. Borwein and F. G. Garvan, Some cubic identities of Ramanujan, Trans. Amer. Math. Soc. 343 (1994), 35-47. Zbl0799.33012
- [7] K. G. Ramanathan, On Ramanujan's continued fraction, Acta Arith. 43 (1984), 209-226. Zbl0535.10007
- [8] K. G. Ramanathan, On some theorems stated by Ramanujan, in: Number Theory and Related Topics, Tata Inst. Fund. Res. Stud. Math. 12, Oxford University Press, Bombay, 1989, 151-160. Zbl0746.11009
- [9] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. Zbl0639.01023
- [10] L. J. Rogers, On a type of modular relation, Proc. London Math. Soc. 19 (1921), 387-397. Zbl48.0151.02
- [11] G. N. Watson, Theorems stated by Ramanujan (VII): theorems on continued fractions, J. London Math. Soc. 4 (1929), 39-48. Zbl55.0273.01
- [12] G. N. Watson, Theorems stated by Ramanujan (IX): two continued fractions, J. London Math. Soc., 231-237. Zbl55.0274.01

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