Timeline for How to implement symbolic Ramanujan's summation in Mathematica?
Current License: CC BY-SA 3.0
7 events
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| May 7, 2015 at 7:37 | comment | added | Anixx | @xzczd this is correct, my comment is somewhat confusing. The ramanujan's sum of g(x)=1 is indeed -0.5. In the comment I meant that I want the Ramanujan's sum of the difference delta. I want a similar formula but giving symbolic results. | |
| May 7, 2015 at 6:45 | comment | added | xzczd♦ |
@Anixx Seems to be another invalid definition: f[x_] = x; g[x_] = DifferenceDelta[f[x], x]; -NSum[ BernoulliB[Floor@n, 1]/n! Derivative[n - 1][g][0], {n, Infinity}] produces -0.5.
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| May 7, 2015 at 6:16 | comment | added | Anixx | @xzczd difference delta, f(x+1)-f(x). | |
| May 7, 2015 at 5:11 | comment | added | xzczd♦ | @Anixx What's the definition of $\Delta[]$? | |
| Apr 21, 2015 at 10:56 | comment | added | Anixx | Ramanujan's summation applies not only to power series, so Zeta regularization is not applicable in the majority of cases. One of the general formulas is $$-\sum_{n=1}^{\infty} \frac{ g^{(n-1)} (0)}{n!} B_n(1)$$ for $g(x)=\Delta [f(x)]$ but how to get it in closed form? | |
| Apr 21, 2015 at 4:00 | history | edited | kirma | CC BY-SA 3.0 |
added 24 characters in body
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| Apr 21, 2015 at 3:43 | history | answered | kirma | CC BY-SA 3.0 |