Timeline for Corner integrals of $\exp$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2018 at 18:30 | comment | added | esg | Note that the final result can be written as $$I=(-1)^n\big( \prod_{i=1}^n A_i\big)\, \Delta^n(\exp(-x);\,0,A_1,\ldots,A_n)$$ where $\Delta^n(f;\,x_0,\ldots,x_n)$ denotes the divided difference of $f$ corresponding to $x_0,\ldots,x_n$. So you can use the calculus of finite differences in your considerations | |
| Jun 12, 2018 at 9:46 | comment | added | Mateusz Kwaśnicki | @WlodAA: You're welcome. I am not a number theorist, I have no idea if this was ever applied there. I think the general case is treated in [Amari, Misra, Closed-Form Expressions for Distribution of Sum of Exponential Random Variables]. | |
| Jun 12, 2018 at 9:20 | comment | added | Wlod AA | The pseudo-singularities due to some equalities $A_k=A_m,\ $ are a bit messy. I wonder if nonstandard analysis would make things smooth? | |
| Jun 12, 2018 at 9:17 | vote | accept | Wlod AA | ||
| Jun 12, 2018 at 9:12 | comment | added | Wlod AA | Thank you, it looks perfect. (It's good I've saved my time asking an expert). I'll get some sleep and will check things exactly after I open my eyes anew. Do you know about number theoretical applications of this material? N.Th. was my motivation. | |
| Jun 12, 2018 at 8:56 | history | answered | Mateusz Kwaśnicki | CC BY-SA 4.0 |