Sectorial fundamental solution (source code)

= 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.