Foias constant
In mathematical analysis, the Foias constant, is a number named after Ciprian Foias.
If x1 > 0 and
then the Foias constant is the unique real number α such that if x1 = α then the sequence diverges to ∞. Numerically, it is
No closed form is known.
When x1 = α then we have the limit:
where "log" denotes the usual natural logarithm.
A fortuitous observation between the prime number theorem and this constant goes as follows,
where π is the prime-counting function.
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