Definition:Foiaș Constant/First

Definition

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 $n \to \infty$.

Decimal Expansion

The decimal expansion of the first Foiaș Constant starts:

$x_{\infty} = 2 \cdotp 29316 \, 62874 \, 11861 \, 03150 \, 80282 \, 91250 \, 80586 \, 43722 \, 57290 \, 32712 \, 12485 \, 37 \ldots$

Also see

• Definition:Second Foiaș Constant

• Results about the Foiaș constants can be found here.

Source of Name

This entry was named for Ciprian Ilie Foiaș.

Sources

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