Timeline for Closed formula for a certain infinite series
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 11, 2021 at 19:04 | history | removed from network questions | Asaf Karagila♦ | ||
| Aug 9, 2021 at 13:24 | vote | accept | T. Amdeberhan | ||
| Aug 9, 2021 at 13:12 | comment | added | T. Amdeberhan | @PietroMajer and Iosif Pinelis: I concur with you. | |
| Aug 9, 2021 at 10:28 | comment | added | Pietro Majer | @Carl-FredrikNybergBrodda ops… I’m a very incorrect reader! :) | |
| Aug 9, 2021 at 10:14 | comment | added | Carl-Fredrik Nyberg Brodda | @PietroMajer Read my comment (and user64494's original) carefully -- I did not write "infinite sum"! :-) | |
| Aug 9, 2021 at 8:50 | comment | added | Carl-Fredrik Nyberg Brodda | @user64494 On the other hand, I think we all agree that an "infinitite sum" is an incorrect math term :-) | |
| Aug 9, 2021 at 7:47 | review | Close votes | |||
| Aug 12, 2021 at 7:50 | |||||
| Aug 9, 2021 at 7:25 | comment | added | Nemo | This question on MathStackExchange asked a similar question: math.stackexchange.com/questions/452028/… The method of solution given there in the accepted answer can be easily applied to the OPs case, similar approach using Mobius transformation. | |
| Aug 9, 2021 at 0:47 | history | became hot network question | |||
| Aug 8, 2021 at 23:20 | comment | added | Pietro Majer | @T. Amdeberhan never follow suggestions from anonymous sources :) | |
| Aug 8, 2021 at 21:08 | answer | added | GH from MO | timeline score: 46 | |
| Aug 8, 2021 at 20:25 | answer | added | Henri Cohen | timeline score: 50 | |
| Aug 8, 2021 at 19:07 | comment | added | Iosif Pinelis | @user64494 : As Pietro Majer said, "infinite sum" is a correct term, and $\sum_{x\in X}f(x)$ can be defined for any (say) real-valued function $f$ on any set $X$. One of a number of mutually equivalent ways to do that is as follows: $\sum_{x\in X}f(x):=\int_X f\,d\nu$, where $\nu$ is the counting measure on (the $\sigma$-algebra of all subsets of) $X$, if the integral exists. | |
| Aug 8, 2021 at 17:57 | comment | added | user64494 | @PietroMajer: An infinite sum cannot be calculated. The question under consideration is about a double series which absolutely converges. | |
| Aug 8, 2021 at 17:53 | comment | added | Pietro Majer | @user64494 why? "infinite sum" is a correct math term, and refers to the sum of a family of numbers, which is the present case. "Sum of a series" is a correct term, yet not applicable here, since the OP's one is not a series. | |
| Aug 8, 2021 at 17:39 | comment | added | user64494 |
Math experiment done with Mathematica Sum[Piecewise[{{Cos[a/b]/a^2/b^2, GCD[a, b] == 1}, {0, True}}], {a, 1, 230}, {b, 1, 230}] // N results in 0.999507. The summation up to $300$ produces $1.00087$.
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| Aug 8, 2021 at 17:32 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
edited title
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| Aug 8, 2021 at 17:29 | comment | added | user64494 | An infinitite sum is an incorrect math term, the sum of a series is a correct one. | |
| Aug 8, 2021 at 16:41 | history | asked | T. Amdeberhan | CC BY-SA 4.0 |