  In the paper, we deal with the problem of getting analytic continuations for
the monomial function associated with a solution to the reduced trinomial
algebraic system. In particular, we develop the idea of applying the
Mellin-Barnes integral representation of the monomial function for solving the
extension problem and demonstrate how to achieve the same result following the
fact that the solution to the universal trinomial system is polyhomogeneous. As
a main result, we construct Puiseux expansions (centred at the origin)
representing analytic continuations of the monomial function.

Complex Variables