Timeline for ζ(-n) and "powers" of Grandi's series
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2017 at 4:17 | history | edited | Aaron Bergman | CC BY-SA 3.0 |
Fixed typos, added more clarity.
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| Apr 4, 2014 at 17:18 | vote | accept | Robin Saunders | ||
| Mar 31, 2014 at 12:05 | history | edited | Aaron Bergman | CC BY-SA 3.0 |
added 8 characters in body
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| Mar 30, 2014 at 23:29 | history | edited | Aaron Bergman | CC BY-SA 3.0 |
Added more details and proofs
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| Feb 28, 2014 at 15:38 | comment | added | Aaron Bergman | Just for fun, it's not too hard to work through higher powers and get a nice formula relating the Bernoulli numbers to the alternating sum of Eulerian numbers which I guess is well-known (ie, on Wikipedia) but was new to me. | |
| Feb 28, 2014 at 3:41 | comment | added | Aaron Bergman | I admit to being a bit lazy on that part -- you can do it by hand for the two functions I gave, but I think it should follow by looking at the smoothing function $A^{-x}$ accounting for the fact that that's not really compactly supported. I'm sure there's a way to do it more generally, but it didn't come to me in the past 24 hours -- I assume it's a standard theorem somewhere, though. | |
| Feb 28, 2014 at 3:25 | comment | added | Sungjin Kim | In Terry Tao's blog post, and in your answer, LHS is being interpreted as partial sum up to $N$ and $N\rightarrow \infty$, but in the power series, they are not partial sums. Indeed, number of terms in the sum is infinite. | |
| Feb 28, 2014 at 3:19 | comment | added | Aaron Bergman | That's in Terry Tao's blog post. | |
| Feb 28, 2014 at 3:14 | comment | added | Sungjin Kim | Does this fully explain OP's question? I think the behavior of the RHS as $x\rightarrow 1$ in power series being the same as LHS interpreted as $\zeta$ values needs to be explained. | |
| Feb 27, 2014 at 21:51 | history | answered | Aaron Bergman | CC BY-SA 3.0 |