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On an Identity of Ramanujan Based on The Hypergeometric Series2F1(13, 23; 12;x)

✍ Scribed by Li-Chien Shen

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 205 KB
Volume: 69
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1997.2212

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✦ Synopsis

Bhargava and F. Garvan provided the first proof to an identity of Ramanujan. Their proof, which is based on various modular identities, is quite difficult and complicated. In this paper, we give a much simpler proof of this identity by converting it into an identity involving the classical elliptic functions and establishing the identity by comparing their Laurent series expansions at a pole.

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