Timeline for How to calculate the infinite sum of this double series?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 25, 2015 at 5:17 | comment | added | Benjamin Dickman | See also: math.stackexchange.com/q/1117583/37122 | |
| Dec 10, 2014 at 9:09 | answer | added | Hjalmar Rosengren | timeline score: 9 | |
| Dec 10, 2014 at 5:47 | history | edited | Lucia |
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| Dec 10, 2014 at 5:31 | answer | added | Lucia | timeline score: 15 | |
| Dec 9, 2014 at 17:01 | comment | added | David E Speyer | I'll try to write something more detailed later, but this reminds me of another sum I wrote about on math.SE where we had a double sum of one over a quadratic with an alternating sign math.stackexchange.com/questions/426325/… | |
| Dec 8, 2014 at 21:58 | comment | added | Alexandre Eremenko | The problem is that your double series in not absolutely convergent. So one cannot interchange the summation, and has to be very careful with what the outer summation means. Stein and Sharkachi textbook on complex analysis addresses this issue and I suppose that a proof can be found there. | |
| Dec 8, 2014 at 16:45 | answer | added | Hachino | timeline score: 2 | |
| Dec 8, 2014 at 16:27 | answer | added | Charles Matthews | timeline score: 0 | |
| Dec 8, 2014 at 16:25 | review | Close votes | |||
| Dec 8, 2014 at 17:12 | |||||
| Dec 8, 2014 at 16:07 | comment | added | tcya | It comes from the probelm 3.48 in Griffiths' <Introduction to Electrodynamics>, 3rd edition. There he met a sum of series $\sum_{n\ odd} \frac{1}{n*sinh (n\pi)}$, which he stated he couldn't find the analytic answer but numerically he got this log and $\pi$ stuff. I'm trying to solve it and I've found it can be converted to the problem of this double sum. | |
| Dec 8, 2014 at 15:12 | comment | added | Jeremy Rouse | How do you know the sum is $\pi \log(2)/16 - \pi^{2}/16$? Also, why are you interested in summing this series? | |
| Dec 8, 2014 at 15:01 | review | First posts | |||
| Dec 8, 2014 at 15:12 | |||||
| Dec 8, 2014 at 14:59 | history | asked | tcya | CC BY-SA 3.0 |