Ramanujan Summation

divergent-series special-functions

It seems that under the light of Ramanujan Summation the following is plausible:

$$1 + {2^{2n - 1}} + {3^{2n - 1}} + \cdots = - \frac{{{B_{2n}}}}{{2n}}(\Re)$$

Alas, I can't really find any concrete definition of Ramanujan Summation. Could someone provide a small explanation?


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...".

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