Timeline for What do named "tricks" share?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 12 at 8:56 | comment | added | Pietro Majer | Yes, this is how physicists usually like to call “connecting the integral to a know one by adding a parameter, and study the dependence from it”, which is something that mathematicians do on a daily base since Newton and Euler. Usually, in the computation, what is the key point for many of them (writing a formula) is the trivial part for a mathematician, and what is the key point for a mathematician (e.g. justifying the passage to the limit) is simply ignored by them as non-physical :P | |
| Jan 19, 2022 at 22:16 | comment | added | Todd Trimble | Thank you, @LSpice! | |
| Jan 19, 2022 at 16:43 | comment | added | LSpice | Titles of @ToddTrimble's references: Almkvist and Zeilberger - The method of differentiating under the integral sign and Chyzak - Creative Telescoping for Parametrised Integration and Summation. | |
| Mar 5, 2017 at 21:26 | comment | added | Todd Trimble | By the way, this "trick" has been promoted to a "method" by Gert Almkvist and Doron Zeilberger: sciencedirect.com/science/article/pii/S0747717108801599 Let me also mention this article, that ties this trick to "creative telescoping" and the Wilf-Zeilberger method: specfun.inria.fr/chyzak/Publications/Chyzak-2012-CTP.pdf | |
| Mar 5, 2017 at 2:55 | comment | added | Włodzimierz Holsztyński | Ooops, before my comment above, the bell function has appeared in @Nate Eldredge's answer. | |
| Mar 2, 2017 at 17:36 | comment | added | Włodzimierz Holsztyński | Another example on introducing an extra variable-the integral of the bell function over $\ \mathbb R\ $ was (is?) popular on American tests and exams. One computes its square as a product of two such integrals but each w.r. to a different variable. Then a student treats it as one integral over $\ \mathbb R^2 $ Then switch to the polar coordinates. | |
| Mar 2, 2017 at 6:31 | comment | added | user78249 | @FanZheng It is essentially this. But by adding the "Feynman" it makes a closer semantic connection to: how effective it is, how it can be used in complicated ways, and that it's even applicable in very advanced scenarios. Especially when you see how Feynman uses it. | |
| Mar 2, 2017 at 5:05 | comment | added | Fan Zheng | This is essentially the "differentiation under the integral sign" trick. I like its application to $\int_0^\infty \sin xdx/x$ best. | |
| Mar 2, 2017 at 3:53 | comment | added | user78249 | @ToddTrimble I know it isn't technically Feynman's (maybe I should've made that clearer), but people have gotten into the swing of calling it Feynman's trick (or Feynman's method; it goes by both names), especially physicists. That's its nomer, and Feynman used it notoriously. I like to call it a trick, because it's really simple and reminds me of a card trick, there's some sleight of hand involved; and that's how it was first called when I heard of it. I also think it's a bit more involved than just Leibniz's integral rule. | |
| Mar 2, 2017 at 3:50 | history | edited | user78249 | CC BY-SA 3.0 |
added 349 characters in body
|
| Mar 2, 2017 at 3:49 | comment | added | Todd Trimble | I wouldn't attribute this "trick" (method?) to Feynman, although he helped to raise awareness of it. en.wikipedia.org/wiki/Leibniz_integral_rule#Examples | |
| S Mar 2, 2017 at 3:27 | history | answered | user78249 | CC BY-SA 3.0 | |
| S Mar 2, 2017 at 3:27 | history | made wiki | Post Made Community Wiki by user78249 |