Timeline for Summation methods for divergent series
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2020 at 5:11 | comment | added | Ilya Zakharevich | It seems one may need to clarify Tom’s comment: in “contemporary terms”, these topics are formalized using notions like “alien derivative” Δ (and the corresponding automorphisms ℜₜ ≔ exp tΔ). Twisting by ℜₜ corresponds to different ways to sum a sequence (or a series). (At least) in many situations, among these twists there is “the central one” — which has “better properties” than the rest. | |
| Mar 25, 2010 at 18:00 | comment | added | Dan Piponi | @Tom While I agree that the sum is morally ${1\over 2}$, I'm tempted to call your bluff on the "That's not quite as flippant as it sounds" claim. :-) | |
| Mar 25, 2010 at 8:23 | comment | added | Tom Leinster | As John Baez has pointed out, the people who claim its value is 0 and the people who claim its value is 1 should compromise and call it 1/2. (That's not quite as flippant as it sounds.) | |
| Mar 25, 2010 at 3:34 | comment | added | Pete L. Clark | I agree with Qiaochu -- certainly some people have claimed that its value is 0, and others (sometimes even the same people!) have claimed that its value is 1. But we're talking about summation methods, not summation opinions. Every summation method I know (that's about 3 or so) gives $\frac{1}{2}$ for this series. | |
| Mar 25, 2010 at 0:08 | comment | added | Qiaochu Yuan | I think it is nowadays accepted that the "correct" value, such as it is, is 1/2. Is there any modern contention of this value? | |
| Mar 24, 2010 at 17:45 | history | answered | Dan Piponi | CC BY-SA 2.5 |