Timeline for A double sum with complex numbers having stochastic variables
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 7, 2022 at 16:39 | comment | added | CfourPiO | Thank you so much for the answer again. It gave me a lot of perspective. My simulations agree with this. | |
| Dec 7, 2022 at 13:41 | vote | accept | CfourPiO | ||
| Dec 6, 2022 at 11:49 | comment | added | Carlo Beenakker | the expression on the second line is an exact evaluation of the integral on the first line; it increases linearly in $N$, with a slope of $M\times \sqrt{2\pi}$. | |
| Dec 6, 2022 at 11:43 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
deleted 2 characters in body
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| Dec 6, 2022 at 10:10 | comment | added | CfourPiO | Also the final term looks like it is a divergent sum, am I correct? I quickly did a simulation with respect to $N$ and it looks like it diverges quickly. | |
| Dec 6, 2022 at 9:55 | comment | added | CfourPiO | Thank you! However, when I look for the geometric series sum $\exp(ixk/2)$ from $k=0$ to $k=N-1$, I see that it is $ \frac{\cos(1/4 (1 + N) x) \sin((N x)/4)}{ \sin(x/4)} + i \frac{sin((N x)/4) sin(1/4 (1 + N) x)} {sin(x/4)}$ in a trigonometric form. It is a complex expression. Did you mean that it can be written in a different way, or did you mean it is this exact sum? | |
| Dec 5, 2022 at 21:38 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |