Talk:Foias constant

Mathematics Stub‑class Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Stub	This article has been rated as Stub-class on Wikipedia's content assessment scale.
Low	This article has been rated as Low-priority on the project's priority scale.

Link to/from List of unsolved problems in mathematics?

If no closed form is known this could be a link to/from this article (Foias constant) to that one? M∧Ŝc²ħε И_τlk 17:31, 12 August 2013 (UTC)[reply]

Table?

Can we have a table of the first 10 values of the sequence with the first one being x_1 = α and other values as to show how this number differs? I am sure the readers do not understand what is going on without a table. John W. Nicholson (talk) 20:36, 22 November 2013 (UTC)[reply]

I made a spreadsheet. It appears that when x₁=α, the sequence increases monotonically at a slowly decreasing rate, but when x₁ is any other positive number, the sequence eventually goes up and down, with the down numbers approaching 1 and the up numbers increasing exponentially. For x₁=1.18, the first decrease occurs at x₁₃; for x₁=1.2, it occurs at x₁₄. phma (talk) 11:40, 23 February 2017 (UTC)[reply]

What happens on other start values?

"If x1 > 0 […] then the Foias constant is the unique real number α such that if x1 = α then the sequence diverges to infinity."

And what happens with that sequence if x_1 is not that special α? --RokerHRO (talk) 09:24, 21 September 2018 (UTC)[reply]

@RokerHRO: I believe it oscillates between values near 1 and large values, but I agree that it would be good to see if this information is contained in one of the references and to add it to the article. --JBL (talk) 12:01, 21 September 2018 (UTC)[reply]

Unique choice?

I've tried x_1=1 and the sequence diverges too... Infovarius (talk) 14:49, 22 October 2021 (UTC)[reply]