Timeline for Are the coefficients in the stationary phase approximation computed explicitly somewhere
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 24 at 23:35 | comment | added | Gary | See $(2.3.23)$ in the DLMF. | |
| Mar 23 at 17:04 | answer | added | James | timeline score: 3 | |
| Mar 22 at 8:14 | comment | added | Piero D'Ancona | I have in my notes that $|a_0|\simeq|\phi^{(k)}(x_0)|^{1/k}|\psi(x_0)|$ but I can not guarantee 100% that the computation was correct :D | |
| Mar 21 at 20:23 | comment | added | Yimin | R. Wong's book "Asymptotic Approximations of Integrals" (epubs.siam.org/doi/book/10.1137/1.9780898719260) has a few sections about this. I think It gave a way to find the coefficients (at least for $k=2$). For $k>2$, I do not have any references but I believe special cases might be known somewhere, for instance $\phi=x^3$, the book has a little related discussion for that in section VII.4. | |
| Mar 20 at 17:22 | comment | added | Medo | Thank you, but I found nothing useful in those references. | |
| Mar 20 at 17:20 | history | undeleted | Medo | ||
| Mar 20 at 17:19 | history | deleted | Medo | via Vote | |
| Mar 19 at 13:18 | comment | added | Abdelmalek Abdesselam | For $k=2$ this is the whole point of the expansion into Feynman diagrams. See Chapters 2 and 3 of the course notes by Etingof ocw.mit.edu/courses/… For $k\ge 3$, explicit formulas are harder to come by. For some work in this direction see this article by Morozov and Shakirov iopscience.iop.org/article/10.1088/1126-6708/2009/12/002 on what they call integral discriminants. | |
| Mar 18 at 22:47 | history | asked | Medo | CC BY-SA 4.0 |