J. M. Borwein, P. B. Borwein, D. H. Bailey, Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi, The American Mathematical Monthly, Vol. 96, No. 3 (Mar., 1989), pp. 201-219
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Borwein et al. (1989) studied this question.
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