On the functional equation $f(p(z))=g(q(z))$, where $p$ and $q$ are “generalized” polynomials and $f$ and $g$ are meromorphic functions

We find all the solutions of the equation $f(p(z))=g(q(z))$, where $p$ and $q$ are polynomials and $p$ and $q$ are transcendental meromorphic functions in $\mathbb C$. In fact, a more general algebraic problem is solved.