Analytic continuation for solutions to the system of trinomial algebraic equations

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.