Sectorial fundamental solution

At an unramified irregular singular point with distinct leading eigenvalues, a sectorial fundamental solution is a fundamental matrix whose entries are holomorphic functions asymptotic to a prescribed formal matrix on a sector of the logarithm cover. For competing cubic exponentials, the usual construction uses six overlapping sectors with basic angle $\pi /3$. A formal power series need not converge, and two sectorial realizations may differ by exponentially small terms across a sector boundary.