Timeline for Why is $ \frac{\pi^2}{12}=\ln(2)$ not true?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Jun 10, 2010 at 20:36 | comment | added | Max Lonysa Muller | Although I think Hardy's book might be a bit too difficult for me at the moment... | |
| Jun 10, 2010 at 18:30 | comment | added | Max Lonysa Muller | I thank both of you for the references! I think I'll have some good reading for the summer holidays... | |
| Jun 10, 2010 at 17:52 | comment | added | Franz Lemmermeyer | I was of course thinking of zeta functions, L-series and theta functions. For methods of assigning finite values to interesting divergent sums (as well as for plenty of other reasons as well), I strongly advise you to read <em>Euler through time: a new look at old themes</em> by Varadarajan. | |
| Jun 10, 2010 at 15:17 | comment | added | Gerald Edgar | values for divergent series ... see Hardy's book, DIVERGENT SERIES | |
| Jun 10, 2010 at 13:44 | comment | added | Max Lonysa Muller | P.S. I'm not sure why (some) functions are most interesting at those places where convergence fails... could you please explain? I am very interested in transforming divergent to convergent series, though, to make the double product equal the single product (and sin(x)/x). Do you think this is possible, one way or another? Or do you know any texts/papers on this subject matter? | |
| Jun 10, 2010 at 13:31 | comment | added | Max Lonysa Muller | Thank you for the reference! As for the different pairing methods, that was what I was thinking about as well... An infinite amount of different (infinite) sum series would all converge to the same value! By the way, do you think there's a way to describe my double product formula in a closed form? I know it diverges, so perhaps it could be an exponential function? Like sin(x)^x? | |
| Jun 10, 2010 at 11:33 | history | answered | Franz Lemmermeyer | CC BY-SA 2.5 |