Embree–Trefethen constant

The Embree - Trefethen constant is a mathematical constant. It is a boundary coefficient in number theory and is denoted by β *.

For a fixed real β, consider the recursion

Where the sign in the sum independent for each n with equal probability as ' ' or '-' is selected.

For β = 1, the random Fibonacci sequence is obtained.

It can be shown that for any of the threshold β

Almost certainly exist. In other words, the result is the same with probability 1 asymptotically exponentially with base σ ( β ).

It is

So falls the sequence of xn almost surely asymptotically exponential, and

So almost certainly the followers grow asymptotically exponentially.

Special values ​​of σ are:

• σ (1) = 1.13198 82487 943 ... ( Viswanath 's constant ) and
• σ ( β * ) = 1