Ramanujan Summation

Ramanujan's Theory of Summation is presented by Bruce C. Berndt in Ramanujan's Notebooks Vol 1, Chapter 6 titled "Ramanujan's Theory of Divergent Series".

A Google search for "Ramanujan's Theory of Summation" gives this Wikipedia article (among others):

http://en.wikipedia.org/wiki/Ramanujan_summation

It states that "Ramanujan summation ..." takes "the Euler–Maclaurin summation formula together with the correction rule using Bernoulli numbers...".