Talk:Kelvin function

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Kelvin function

This seems meaningless to me. I believe that a Kelvin function is actually a form of Bessel function (in mathematics - nothing to do with temperature). SemperBlotto 22:17, 2 March 2007 (UTC)

Well I think we need an expert for this one - lots of Google book hits, none of which shed any light on the meaning of the term for me - e.g.:

Sergej L. Sobolev, Raymond Bonnett, Cubature Formulas and Modern Analysis: An Introduction (1993) p. 164:

Hence it follows immediately that under a rotation of the system of coordinates, an arbitrary Kelvin function passes into a Kelvin function.

B Straughan, R Greve, H Ehrentraut, Continuum Mechanics and Applications in Geophysics and the Environment (2001) p. 313:

kei (.) is a Kelvin function of zero order, which can be derived from the general Bessel function, and whose values are tabulated.

...

The Kelvin function takes the value zero at approximately r = 4L_r, followed by a slight forebuldge (upward displacement) further away from the load.

These bring to my mind a picture of a group of scientists studying a graph, one of whom says, "ah, a Kelvin function," prompting the others to nod and murmer, "yes, yes, of course, Kelvin function. Good show." It does come up in context with a Bessel function a lot. What the heck is a Bessel function? bd2412 T 22:31, 2 March 2007 (UTC)

I rewrote the definition according as this article [1]. Please could someone review it... --Tohru 04:23, 3 March 2007 (UTC)

An appreciable effort, but still incomprehensible to me - I have no doubt the phrase is a legitimate subset of Bessel functions, but what do the ber and bei mean? bd2412 T 07:18, 3 March 2007 (UTC)

For a possible answer to the question, you don't have to bother about the meanings of ber and bei; they are just conventionally used labels for the two functions that are defined in the article, and there are no further assumptions. I modified the definition trying to clarify the point. Personally, I infer that the first two letters "be" might be abbreviated "Bessel", and that the following "r" and "i" probably came from the first letter of "real part" and "imaginary part".

By the way I used to use Bessel functions quite often throughout my graduate course in theoretical physics almost ten years ago. While I remember the Neumann function and the Hankel function as the sister functions, I don't know if I've ever heard of this one. It must be a considerably minor type. --Tohru 10:22, 3 March 2007 (UTC)

From the MathWorld article, it appears that the Kelvin functions are simply the solutions to the Kelvin differential equation, x²y''+xy'-(ix²+v²)y=0. DAVilla 20:18, 8 March 2007 (UTC)

You can simply say that a Bessel function is a solution of a Bessel differential equation, but meanwhile either a solo Kelvin function ber_n(x), bei_n(x), ker_n(x) or kei_n(x) doesn't satisfy a Kelvin differential equation. Only a particular combination of them like ber_n(x) + i bei_n(x) or ker_n(x) + i kei_n(x) does, according to the article [2]. A more careful treatment than one for Bessel functions is needed here. --Tohru 07:50, 9 March 2007 (UTC)

To give a simple example, if I were to define a triangular number as a number of the form n(n+1)/2 for integer n, then it would give absolutely no insight at all into why this would ever be of any interest. Explain the significance in English first, and then provide the formulas. DAVilla 19:41, 9 March 2007 (UTC)

OK, thank you for the valuable feedbacks. I revised it again taking your suggestion into consideration. I feel it is much improved. --Tohru 02:50, 11 March 2007 (UTC)

Struck. Seems to have been resolved. — Beobach972 15:43, 5 June 2007 (UTC)