Timeline for What do named "tricks" share?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 28 at 18:21 | comment | added | The Tiler | As a math fan, it seems to me that to find the value of $\Gamma(z) \Gamma(1-z)$, V.Smirnov used the same trick and then calculated $\Gamma(\frac{1}{2})=\srqt{ \pi} $. See: archive.org/details/… | |
| Jun 28 at 15:01 | history | edited | Michael Hardy | CC BY-SA 4.0 |
better MathJax usage
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| Feb 11, 2022 at 13:39 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Jan 20, 2022 at 5:49 | history | edited | Nate Eldredge | CC BY-SA 4.0 |
citation link
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| Jan 19, 2022 at 23:05 | comment | added | LSpice | References, clickably: Dawson - On a "singular" integration trick of Possion; Georgakis - A note on the Gaussian integral (mentioned by @MichaelHardy). | |
| Aug 23, 2021 at 22:32 | comment | added | Oscar Lanzi | For a different version of this trick, in which we use a Cartesian-to-Cartesian transformation, see here. | |
| Mar 26, 2012 at 3:15 | comment | added | KConrad | @Michael Hardy: that "better alternative" in the paper by Georgakis in fact is due to Laplace. See york.ac.uk/depts/maths/histstat/normal_history.pdf. | |
| Jul 9, 2011 at 6:11 | comment | added | Noam D. Elkies | While the specific form $f(x) f(y) = g(\sqrt{x^2+y^2})$ applies only to Gaussians, there are further uses of this kind of transformation: in one direction, to the volumes of Euclidean spheres in higher dimension (imagine you already know $\Gamma(1/2)$ but not the area of a circle); in another direction, to the usual proof of $B(x,y) = \Gamma(x) \Gamma(y) / \Gamma(x+y)$; combining these, to Dirichlet integrals; and by analogue, to the relation between Gauss sums and Jacobi sums — and probably others that don't come to mind right now. | |
| Dec 5, 2010 at 22:19 | comment | added | Michael Hardy | Constantine Georgakis, "A Note on the Gaussian Integral", Mathematics Magazine, February, 1994, page 47 This paper gives what its author considers "a better alternative to the usual method of reduction to polar coordinates" for evaluating this integral. See en.wikipedia.org/wiki/Gaussian_integral . | |
| Dec 5, 2010 at 22:17 | comment | added | Michael Hardy | I think Dawson was anticipated by James Clerk Maxwell. A result called Maxwell's theorem says that if $X_1, \dots, X_n$ are independent real-valued random variables and their joint density is spherically symmetric, then all of them are normally distributed, i.e. the probability density of each of them is a Gaussian function. | |
| Dec 5, 2010 at 22:04 | comment | added | darij grinberg | Note that this trick has something in common with the Rabinowitsch, Cayley and Eilenberg tricks and probably some others on the list: in order to solve a $k$-dimensional problem, you go into more than $k$ dimensions. This also seems to be a distinguishing feature of things called tricks. | |
| Dec 5, 2010 at 21:59 | history | answered | Nate Eldredge | CC BY-SA 2.5 |