In mathematics, the Prouhet–Thue–Morse constant, named for Eugène Prouhet, Axel Thue, and Marston Morse, is the number—denoted by
where
The generating series for the
and can be expressed as
This is the product of Frobenius polynomials, and thus generalizes to arbitrary fields.
The Prouhet–Thue–Morse constant was shown to be transcendental by Kurt Mahler in 1929.
References
Prouhet–Thue–Morse constant Wikipedia(Text) CC BY-SA