Talk:Gaussian Integral

I agree on the merge suggestion. --Alec (talk) 19:47, 21 March 2011 (CDT)

New Definition
Regarding:


 * $\displaystyle \phi\left({-\infty, +\infty}\right) = \int_{\to -\infty}^{\to +\infty} \frac 1 {\sqrt{2\pi}} \exp \left({- \frac 1 2 x}\right) \, \mathrm dx = 1$

where $\phi$ is as defined in Definition:Gaussian Integral/Two Variables.

With the new definitions I'm putting it up, it would be useful to have that theorem as what is currently this page, and then I would like to rename this page's theorem to... something else I haven't thought of. In particular, I need that result to prove $\phi$ is a probability measure. Is swapping names like that a good idea? Or should I make one a corollary of the other? --GFauxPas (talk) 13:12, 12 February 2013 (UTC)


 * There are indeed a few standard definitions for "Gaussian". Yours is usual from the perspective of measure theory. I'm more used to the definition currently given, which arises in association with the Gamma function. --Lord_Farin (talk) 14:40, 12 February 2013 (UTC)


 * So, disambiguate "Gaussian"? If so, we'd need (arbitrarily chosen, perhaps) more specific names for each kind. Also, I'm limited in that my only sources for this stuff are probability and statistics texts. --GFauxPas (talk) 15:23, 12 February 2013 (UTC)


 * If the two usages of "Gaussian" basically describe variants of the same concept, then rather than disambiguation we are better off by transcluding. --prime mover (talk) 15:30, 12 February 2013 (UTC)


 * Agreed. --Lord_Farin (talk) 15:38, 12 February 2013 (UTC)


 * So, as to my original question...? --GFauxPas (talk) 15:56, 12 February 2013 (UTC)


 * 't Is a bit of a difficult call. I think my preference is to have a transclusion of subpages (where the second subpage possibly uses the first in its proof, for brevity). --Lord_Farin (talk) 17:09, 12 February 2013 (UTC)

How 'bout Gaussian Integral (Variant 1) and so on? --GFauxPas (talk) 20:04, 12 February 2013 (UTC)


 * IMHO such "numbering" should be restrained in full page names and be relegated to subpages instead. As for linking to these subpages there's perhaps a need for good names, but we can always just give the full link like with most "General Result" sections. --Lord_Farin (talk) 21:11, 12 February 2013 (UTC)


 * I started constructing, any contributor should feel free to stop what I'm doing at any point to suggest a cleaner route as I go forward. --GFauxPas (talk) 13:46, 14 February 2013 (UTC)