Talk:Prolate spheroidal wave function

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	This article was accepted on 17 September 2007 by reviewer Graeme Bartlett (talk · contribs).

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Contrary to what the first paragraph claims, the PSWFs are not time-limited. If $\psi _{n}$ were in fact time-limited, the second $Q_{T}$ in the expression $Q_{T}P_{W}Q_{T}\psi _{n}=\lambda _{n}\psi _{n}$ would be redundant anyway. Based on the original paper by Slepian and Pollack, and using the notation established in this article, the correct expression seems to be

P_{W}Q_{T}\psi _{n}=\lambda _{n}\psi _{n}

where $\psi _{n}$ are bandlimited. Perhaps somebody with more background in this matter can confirm this. Qopzm (talk) 00:39, 8 July 2010 (UTC)[reply]

I agree

I agree with this observation, that the PSWF's are not time limited. In fact, they are defined to be those functions which maximise the power contained the region [-T,T] given the constraint that they have unit power on R. I have constructed explicitly these functions and they do not vanish outside a compact interval. Indeed, it is a general result that a function which vanishes on a compact interval necessarily cannot have a frequency content which vanished on a compact interval. I will work on the revision to this incorrect material. angusprain 18:25, 1 March 2013.

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Order of material: re-written

List of changes:

Headings inserted, paragraphs re-ordered in more natural way
Application on band-limited functions shifted to the middle
In that section, time interval set to $-T\ldots T$ , as in NIST's Digital Library of Mathematical Functions (DLMF) §30.15 (reference added)
The explicit form of the band-limited eigenfunctions given in terms of angular PSWF
Correction: the PSWF are not time-limited, but band-limited
The convention for prolate coordinates modified as in the corresponding wiki page
Dead links to Slepian & el papers replaced by DOI
The eigenvalue $\lambda _{mn}(c)$ is fixed by the boundary values of the angular function at $\eta =\pm 1$ , and not by the behaviour of the radial function (see DLMF §30.13)
References tidied up: include page numbers, bibliographic information: journal_name vol (year) page.

Further improvements:

Wouldn't it be useful to visualise the prolate functions? The DLMF gives simple cross sections in the coordinates $\xi$ and $\eta$ , but it would be great to show a true spheroid. Needs some 3D plotting.

--DieHenkels (talk) 12:54, 20 May 2021 (UTC)[reply]

Oblate spheroidal wave function

The article was apparently drafted by the same team as the prolate functions. Similar changes appear natural, since the two sets of functions are intimately related. --DieHenkels (talk) 12:54, 20 May 2021 (UTC)[reply]