Talk:Gaussian function

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Do we mean to say that

gaussian functions are eigenfunctions of the Fourier transform,

or that

eigenfunctions of the Fourier transform are gaussian functions

or neither? -- Miguel

Not all eigenfunctions of the Fourier transform are Gaussian. See Hermite polynomials. Michael Hardy 15:10, 30 Aug 2003 (UTC)

Contents

[edit] maximum entropy

Could someone add something about Gaussian functions being the ones with maximum entropy? I think this can also be related to the Heisenberg uncertainty principle since momentum and position are canonical conjugate variables.

This article links to normal distribution, which I suspect already gives that information. For non-normalized Gaussian functions, I'm not sure at this moment what the maximum-entropy statement would say. Michael Hardy 23:46, 27 Feb 2005 (UTC)

[edit] image

are they all the same bell-shape? if so, let's get a picture! - Omegatron 17:51, Mar 15, 2005 (UTC)

[edit] Definition of μ,σ

The function definition uses a,b,c as parameters, while the graph uses μ,σ as parameters. What is the relation between the two sets of parameters?

--NeilenMarais 20:18, 24 May 2006 (UTC)

Answering myself, it seems from looking at Gaussian function that a=\frac{1}{\sigma\sqrt{2\pi}}, b = μ and c=\sqrt{2}\sigma. One could mention this, or perhaps even better, generate an image using the correct parameters. Opinions? --NeilenMarais 20:27, 24 May 2006 (UTC)

Not entirely correct. Not all Gaussian functions are probability density functions, so a need not be a normalizing constant that makes the integral equal to 1.

But certainly I think the caption should explain the notation used in the illustration. Michael Hardy 21:29, 24 May 2006 (UTC)

[edit] Gaussian Function ..

Would I be correct if i said that a gaussian function as such represents the values a variable can have .............that is to say ......it gives us a range of possible values of the variable , or it shows the region were the value of that variable lies ......

Is that what the Gaussian function does ... —The preceding unsigned comment was added by Hari krishnan07 (talk • contribs) 04:36, 3 December 2006 (UTC).

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