Some of the most spectacular achievements in the history of the number π are the representations of 1/π by rapidly converging series discovered by Ramanujan in 1914. Although Ramanujan himself did not explain how he arrived at his series, he indicated that they belong to what is now known as ‘the theories of elliptic functions to alternative bases’. The first rigorous mathematical proofs of Ramanujan’s identities in and generalizations of them were given by the Borweins and the Chudnovskys.
Russian Mathematical Surveys Vol. 62, Issue 3, p. 634-636
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