Summary: Euler, Pisot, Prouhet-Thue-Morse, Wallis
and the duplication of sines
J.-P. Allouche
CNRS, LRI, UMR 8623
Universit´e Paris-Sud, B^atiment 490
F-91405 Orsay Cedex
France
allouche@lri.fr
M. Mend`es France
Universit´e Bordeaux I
Math´ematiques
F-33405 Talence Cedex
France
michel.mendes-france@math.u-bordeaux1.fr
Abstract
We all know Euler's product (1 + X2n
) = (1 - X)-1 and its
companion (1 - X2n
) = ±Xj, where the sequence of signs
is the so-called Prouhet-Thue-Morse automatic sequence. Dis-

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

Collections: Computer Technologies and Information Sciences