If have a function $f$ given by a series $$ f(z) = \sum_{n,m = 0}^\infty u_{n,m} z^{n + m t} $$ for some $t\in\mathbb{R}^+$.
Is there an straightforward way (something similar to the inversion formula for Taylor series) to derive a similar series for $f^{-1}(z)$?