A power series f is said to satisfy a p-Mahler equation (p>1 a natural number) if it satisfies a functional equation of the form
a_n(x).f(x^{p^n}) + ... + a_1(x).f(x^p) + a_0(x).f(x) = 0
where the coefficients a_i(x) are polynomials. These functional equations were studied by Kurt Mahler with relation to transcendence theory.
