Category:Definitions/Foiaș Constants

This category contains definitions related to Foiaș Constants.
Related results can be found in Category:Foiaș Constants.

First Foiaș Constant

Let:

$x_{n + 1} = \paren {1 + \dfrac 1 {x_n} }^{x_n}$

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:

$x_{n + 1} = \paren {1 + \dfrac 1 {x_n} }^n$

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.