\begin{definition}[Definition:Feigenbaum Constants/First]
The '''first Feigenbaum constant''' is the limiting ratio of each bifurcation interval to the next between every period doubling of a one-parameter mapping:
:$x_{i + 1} = \map f {x_i}$
where $\map f x$ is a function parameterized by the bifurcation parameter $a$.
It is given by the limit:
:$\ds \delta = \lim_{n \mathop \to \infty} \dfrac{a_ {n - 1} - a_{n - 2} } {a_n - a_{n - 1} } = 4 \cdotp 66920 \, 16091 \, 02990 \, 67185 \, 32038 \, 20466 \, 20161 \, 72 \ldots$
where $a_n$ are discrete values of $a$ at the $n$th period doubling.
Its precise value appears to be a topic of research, as various resources quote it differently from the above, including the {{AuthorRef|David Wells}} $1997$ source work {{BookLink|Curious and Interesting Numbers|David Wells|ed = 2nd|edpage = Second Edition}}.
{{OEIS|A006890}}
\end{definition}