Ramanujan’s Theories of Elliptic Functions to Alternative Bases

Berndt, B. C. and Bhargava, S. and Garvan, F. G. (1995) Ramanujan’s Theories of Elliptic Functions to Alternative Bases. Transactions of the American Mathematical Society, 347 (11). pp. 4163-4244.

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Official URL: https://doi.org/10.2307/2155035


In his famous paper on modular equations and approximations to pi, Ramanujan offers several series representations for 1/pi, which he claims are derived from `'corresponding theories'' in which the classical base q is replaced by one of three other bases. The formulas for 1/pi were only recently proved by J. M. and P. B. Borwein in 1987, but these `'corresponding theories'' have never been heretofore developed. However, on six pages of his notebooks, Ramanujan gives approximately 50 results without proofs in these theories. The purpose of this paper is to prove all of these claims, and several further results are established as well.

Item Type: Article
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: Users 23 not found.
Date Deposited: 21 May 2021 06:17
Last Modified: 16 Jun 2022 11:36
URI: http://eprints.uni-mysore.ac.in/id/eprint/16485

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