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Thursday, November 7, 2013

**Abstract:** On page 336 in his lost notebook, S. Ramanujan proposes an identity that may have been devised to attack a divisor problem. Unfortunately, the identity is vitiated by a divergent series appearing in it. We prove here a corrected version of Ramanujan's identity. We also show its connection to an infinite series involving the modified Bessel function $K_{s}(x)$. We will also discuss a related series identity due to Ramanujan and S. Wigert along with its new generalization. This is joint work with Bruce C. Berndt, Arindam Roy and Alexandru Zaharescu.