Feller's coin-tossing constants
From Wikipedia, the free encyclopedia
Feller's coin-tossing constants are a set of numerical constants which describe asymptotic probabilities that in n independent tosses of a fair coin, no run of k consecutive heads (or, equally, tails) appears.
William Feller showed[1] that if this probability is written as p(n,k) then
where αk is the smallest positive real root of
and