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The first Feigenbaum constant or simply Feigenbaum constant^[5] δ is the limiting ratio of each bifurcation interval to the next between every period doubling, of a one-parameter map

${\displaystyle x_{i+1}=f(x_i),}$

where f (x) is a function parameterized by the bifurcation parameter a.

It is given by the limit:^[6]

${\displaystyle \delta =\underset{n\to \mathrm{\infty }}{lim}\frac{a_{n-1}-a_{n-2}}{a_n-a_{n-1}}}$

where a_n are discrete values of a at the nth period doubling.

This gives its numerical value (sequence A006890 in the OEIS):

${\displaystyle \delta =4.669201609102990671853203820466\dots }$