On Ramanujan's cubic continued fraction

• Autorzy: Heng Huat Chan
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 73
• Numer: 4
• Strony: 343-355

Daty

wydano

1995

otrzymano

1994-05-04

poprawiono

1995-02-07

Twórcy

autor

Heng Huat Chan

• Department of Mathematics, University of Illinois, 273 Altgeld Hall, 1409 West Green Street, Urbana, Illinois 61801, U.S.A.

Bibliografia

• [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).
• [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.
• [6] J. M. Borwein, P. B. Borwein and F. G. Garvan, Some cubic identities of Ramanujan, Trans. Amer. Math. Soc. 343 (1994), 35-47.
• [7] K. G. Ramanathan, On Ramanujan's continued fraction, Acta Arith. 43 (1984), 209-226.
• [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.
• [9] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.
• [10] L. J. Rogers, On a type of modular relation, Proc. London Math. Soc. 19 (1921), 387-397.
• [11] G. N. Watson, Theorems stated by Ramanujan (VII): theorems on continued fractions, J. London Math. Soc. 4 (1929), 39-48.
• [12] G. N. Watson, Theorems stated by Ramanujan (IX): two continued fractions, J. London Math. Soc., 231-237.