Foias constant

In mathematical analysis, the Foias constant is a real number named after Ciprian Foias.

For all other values of x1, the sequence is divergent as well, but it has two accumulation points: 1 and infinity.

[1] Numerically, it is No closed form for the constant is known.

When x1 = α then the growth rate of the sequence (xn) is given by the limit where "log" denotes the natural logarithm.

[1] The same methods used in the proof of the uniqueness of the Foias constant may also be applied to other similar recursive sequences.

Evolution of the sequence for several values of , around the Foias constant . Evolution for is in green. Other initial values lead to two accumulation points, 1 and . A logarithmic scale is used.