Timeline for Where do these divergent integrals appear in mathematics and physics?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2021 at 10:07 | comment | added | Anixx | The linked paper seems to have errors, and I have identified at least two. The monomials should regularize to zero in fact. I wonder, what is the source for the first integral? | |
| Jun 6, 2021 at 17:26 | comment | added | Anixx | Is there a source for the first integral? | |
| Jun 6, 2021 at 12:01 | comment | added | Carlo Beenakker | mathoverflow.net/questions/394643/… | |
| Jun 6, 2021 at 10:51 | comment | added | Anixx | The regularization value of 0 can be verified with Mathematica: f[x_] := x^p; Limit[s Sum[f[s x],{x,1,Infinity},Regularization->"Dirichlet"],s->0] | |
| Jun 6, 2021 at 10:29 | comment | added | Anixx | I have the following formula: $\int_0^\infty x^n dx=\frac{\left(\tau +\frac{1}{2}\right)^{n+2}-\left(\tau -\frac{1}{2}\right)^{n+2}}{(n+1)(n+2)}=\frac{\omega _+^{n+2}-\omega _-^{n+2}}{(n+1)(n+2)}$ which regularizes to $\frac{B_{n+2}(1)-B_{n+2}(0)}{(n+1)(n+2)}$, which is zero. Integrals of monomials always regularize rto zero as far as I know. | |
| Jun 5, 2021 at 3:49 | comment | added | Piotr Hajlasz | More details to your interesting answer are welcome. I am sure you, as a physicist can do it. Otherwise from the mathematical point of view your answer is along the medieval proof of the existence of God: 0=(1-1)+(1-1)+...=1+(-1+1)+(-1+1)+...=1. Something was created from nothing. God exists!!! | |
| Jun 4, 2021 at 4:58 | comment | added | Anixx | Hmm, this is not in line with the regularization methods I know, on my clock, an integral of monomial from 0 to infinity regularizes to 0. | |
| Jun 2, 2021 at 17:05 | comment | added | Carlo Beenakker | "=" because I am too timid to write $\int_0^\infty x\,dx=1/6$. | |
| Jun 2, 2021 at 16:24 | comment | added | Soleil | Why is the = double quoted ? | |
| Jun 2, 2021 at 12:33 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |