Timeline for Are there any known approaches of generalizing functions that do not have a limit at infinity to values at infinity?
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13 events
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| Jul 5, 2017 at 17:54 | comment | added | Anixx | By the way, when $k=0$ the integral should be simply $\pi\delta(0)$. Is it the case where notation $\cal P$ plays role? | |
| Jul 5, 2017 at 16:04 | comment | added | Carlo Beenakker | the Wikipedia article has several applications of the Sokhotski–Plemelj integral relation, and a Google search gives many more pointers; a Fourier-transform formulation is here (appendix). | |
| Jul 5, 2017 at 15:56 | comment | added | Anixx | Oh, possibly I understood now, in this notation $\cal P$ is not a factor, so we can simply disregard it. But does this method allow to integrate an arbitrary function (or at least, could we obtain values better than in Fourier transform?) | |
| Jul 5, 2017 at 15:36 | comment | added | Anixx | Purely logically the integral should be positive because sine function is initially positive. It is analogious to the series 1-1+1-1+... which sums up to 1/2, while if the first term is -1, the sum would be -1/2 | |
| Jul 5, 2017 at 13:42 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 5, 2017 at 13:25 | comment | added | Carlo Beenakker | indeed, my mistake, corrected, thanks; $g(x)$ is an arbitrary function. | |
| Jul 5, 2017 at 13:22 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 5, 2017 at 13:11 | comment | added | Anixx | If you get -1, you definitely made some mistake, I think. It is still unclear though how the first and second formulas are related (what is g(x) for instance). | |
| Jul 5, 2017 at 13:08 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 5, 2017 at 12:55 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 5, 2017 at 12:03 | comment | added | Anixx | Still not clear, principal value of what integral?... | |
| Jul 5, 2017 at 12:01 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 5, 2017 at 11:59 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |