Timeline for Is it possible to sum the divergent series with prime coefficients?
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| Feb 26, 2020 at 14:39 | comment | added | Alex Gavrilov | user76284 @: The analytic continuation of a given function is (more or less) unique, but in this context we not not HAVE a function. We have to chose it and the number of choices is pretty much unlimited. For a reference to the above, see e.g. Hardy, Divergent series, Theorem 9 (p. 52 in the edition I am looking at). | |
| Feb 25, 2020 at 19:10 | comment | added | user76284 | "any other linear regular summation method with positive matrix, are useless when dealing with a series with positive summands: if the original series is not convergent, then the summation does not help." Do you have a reference for this? I also thought analytic continuation was unique. | |
| Aug 27, 2014 at 20:17 | comment | added | Aaron Bergman | Just with regards to the last point, I would say that zeta function regularization works because it is giving the constant term when the divergence is smoothly cut off. I never learned this in my physics courses, though, and when I first read about it on Terry Tao's blog it was a revelation. | |
| Aug 27, 2014 at 14:16 | history | answered | Alex Gavrilov | CC BY-SA 3.0 |