Foias constant
In mathematical analysis, the Foias constant is a real number named after Ciprian Foias.
It is defined in the following way: for every real number x1 > 0, there is a sequence defined by the recurrence relation
for n = 1, 2, 3,.... The Foias constant is the unique choice α such that if x1 = α then the sequence diverges to infinity. Numerically, it is
No closed form for the constant is known.
When x1 = α then we have the limit:
where "log" denotes the natural logarithm. Consequently, one has by the prime number theorem that in this case
where is the prime-counting function.
