Talk:Chebyshev cube root

I just changed the wording "we" > "one" in the beginning of "Motivation" section, but it would be better to use passive voice... Other things that remain to be done: - introduce subsections (half the article is in the "motivation" section) - make the article nicer to read / look at - esp. in the 2nd half, there are too much formulae in the text ! (even if I appreciate technical details in math articles) &mdash; MFH:Talk 18:48, 13 March 2008 (UTC)

Deleting or redirecting this page?
This page has been proposed for deletion on November 6 by the tag { {Proposed deletion/dated|concern = The notion and the content are original research|timestamp = 20101106101217}}. This tag has been removed on November 11 by Michael Hardy with the reason I find seven items via Google Scholar using this term.

Effectively, Google Scholar gives 7 items of papers mentioning Chebyshev cube root, 4 in physic and 3 by the same author in computational geometry. None may be viewed as a source for Chebyshev cube root but one gives a source: Abramowitz, Milton; Stegun, Irene A., eds. (1965), ”Chapter 22”, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover, pp. 773.

Nevertheless the page has several issues:
 * Lacking of source. I have found one source, which I can not consult this week. It seems, from the title of the book, that it is a source for the name of the function and the main formulas, but probably not for the other considerations of the page.
 * Notoriety. The name of Chebyshev cube root has been used recently (Scholar Google said} by only five authors. This appears as a very low notoriety, too low for being the subject of a main page.
 * Non neutral original research. It is asserted in the motivations (first paragraph of Section motivation that Chebyshev cube root behaves better than cubic root. It is a unfounded and non neutral original research, as, for each asserted inconvenience of the cubic root function one may provide a similar inconvenience of the Chebyshev cubic root, as it is defined in the page (I may give details if needed).
 * Lacking of a formal definition of the notion. The Chebyshev cubic root is not formally defined. One may deduce from the text that it is the analytic solution of the equation $$x^3 - 3x = t$$ which is equal to $$\sqrt{3}$$ for $$t=0$$ and is defined everywhere in the complex plane except for real $$t\le -2\,.$$
 * Bad writing. It is almost impossible, unless for an experimented mathematician, to recognize what is a definition, a property or a part of a proof. Moreover to prove analycity, instead of using directly the implicit function theorem, the editor has used a difficult method of gluing two compound analytic functions.

Thus most of the page is original research and/or poor mathematics and deserves to be deleted. Only the name of the notion and the formulas in term of trigonometric and hyperbolic functions deserve to be kept. These formulas almost appear in the section Trigonometric (and hyperbolic) method of cubic function.

Therefore, I propose to redirect Chebyshev cube root to this section, after adding to it something like: When p=-3, the functions defined by these formulas are sometimes named Chebyshev cubic root [reference to Abramowitz]

I intend to do this in the next days. D.Lazard (talk) 21:41, 13 November 2010 (UTC)