\begin{definition}[Definition:Foiaș Constant/Second]
Let $x_1 \in \R_{>0}$ be a (strictly) positive real number.
Let:
:$x_{n + 1} = \paren {1 + \dfrac 1 {x_n} }^n$
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 $\sequence {x_{n + 1} }$ diverges to infinity.
No closed-form expression is known.
\end{definition}