An asymptotic approach in Mahler's method

We provide a general result for the algebraic independence of Mahler functions by a new method based on asymptotic analysis. As a consequence of our method, these results hold not only over C<i>z</i>, but also over C<i>z</i>(<i>M</i>), where (<i>M</i>) is the set of meromorphic functions. Several examples and corollaries are given, with special attention to nonnegative regular functions.