Definition:Foiaș Constant
Check that the actual attributed numbers "first" and "second" for this pair of constants has been defined correctly. I believe the way it has been defined here is wrong. The author of the original page is requested to learn house style before embarking on substantial contributions -- putting it into a readable and usable format is time-consuming and tedious.
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Contents
Definition
First Foiaș Constant
Let:
- $x_{n+1} = \left({1 + \dfrac 1 {x_n} }\right)^{x_n}$
for $n = 1, 2, 3, \ldots$
The first Foiaș constant is the limit of $x_n$ as $n \to \infty$.
Second Foiaș Constant
Let $x_1 \in \R_{>0}$ be a (strictly) positive real number.
Let:
- $x_{n + 1} = \left({1 + \dfrac 1 {x_n} }\right)^n$
for $n = 1, 2, 3, \ldots$
The second Foiaș constant is defined as the unique real number $\alpha$ such that if $x_1 = \alpha$ then the sequence $\left\langle{x_{n + 1} }\right\rangle$ diverges to infinity.
Also known as
Many sources omit the diacritic: Foias.
Some sources refer to the second Foiaș constant as the Foiaș constant.
Source of Name
This entry was named for Ciprian Ilie Foiaș.
