Cubic modular equations and new Ramanujan-type series for 1/π

Pacific Journal of Mathematics

Volumn 192, Issue 2, 2000, Pages 219-238

  Chan, Heng Huat ^a   Liaw, Wen Chin ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013532021     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2000.192.219     Document Type: Article

References (11)

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2. B.C. Berndt, S. Bhargava and F.G. Garvan, Ramanujan's theories of elliptic functions to alternative bases, Trans. Amer. Math. Soc., 347 (1995), 4163-4244.
3. J.M. Borwein and P.B. Borwein, Pi and the AGM, Wiley, New York, 1987.
4. _, Class number three Ramanujan type series for 1/π, J. Comput. Appl. Math., 46 (1993), 281-290.
5. 1(1/3, 2/3; 1; z), Math. Proc. Cambridge Philos. Soc., 124 (1998), 193-204.
6. H.H. Chan and W.-C. Liaw, On Russell-type modular equations, Canad. J. Math., to appear.
7. 2, Wiley, New York, 1989.
8. C.F. Gauss, Disquisitiones Arithmeticae, Springer-Verlag, New York, 1986.
9. K.G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc., 52 (1987), 71-89.
10. S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford), 45 (1914), 350-372.
11. C.L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980.