Talk:Foias constant

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∧Ŝc²ħεИ_τlk 17:31, 12 August 2013 (UTC)

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)

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)

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)

@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)

Unique choice?

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

Yes, but not to infinity. --JBL (talk) 15:27, 22 October 2021 (UTC)

Graph

The graph is wrong. With initial values below and above the constant, the lines should oscillate with opposite phase. Matrix Computations (talk) 11:01, 17 July 2022 (UTC)

Yes it's easy to see in the source code that the file was generated with the wrong recurrence $x_{n+1}=(1+1/x_{n})^{n+1}$ instead of $x_{n+1}=(1+1/x_{n})^{n}$, leading to (for example) the value $x_{2}=4$ when $x_{1}=1$. Pinging the file creator @Jochen Burghardt: to take a look. JBL (talk) 19:59, 17 July 2022 (UTC)