I don't think the use of zeta(-1) = -1/12 in physics has anything to do with these formal manipulations --- they have to do with extending zeta(s) analytically in the complex plane. What's curious is that there is a set of formal manipulations that leads to the same answer. But this may be true for _every_ possible answer. Cris On Mar 1, 2014, at 2:07 PM, David Wilson <davidwwilson@comcast.net> wrote:
Seriously, do physicists routinely use these types of formal manipulations without any mathematical foundation? I'm guessing not. If physicists are using equation like [1] in actual physics, I suspect they must have some theory to justify their methods.
Cristopher Moore Professor, Santa Fe Institute The Nature of Computation Cristopher Moore and Stephan Mertens Available now at all good bookstores, or through Oxford University Press http://www.nature-of-computation.org/