Summary: The Komornik­Loreti constant is transcendental
Jean­Paul Allouche and Michel Cosnard
Let q be a non­integer real number ? 1, and let bqc be its integer part. The sum
1
X
n=0
a n =q n
is called a q­expansion of the positive real number x if
ffl for all n – 0, we have 0 Ÿ a n Ÿ bqc,
ffl x =
1
X
n=0
a n
q n
.
Any real number x such that 0 Ÿ x Ÿ qbqc=(q \Gamma 1) admits such a decomposition (use
the greedy algorithm). But the decomposition is not necessarily unique: for example if
ø = (1 +
p

Source: Allouche, Jean-Paul - Laboratoire de Recherche en Informatique, Université de Paris-Sud 11

Collections: Computer Technologies and Information Sciences