More on asymptotic approximation for matrix differential equations (Q1284025)

By means of WKB-methods, an asymptotic approximation is obtained for the solution of \(Y''=t^hA(t)Y\), where \(h\) is a real number, and \(A(t)\) a Hermitean \(n\times n\)-matrix for real \(t\), which is analytic and invertible on \((a,\infty]\). The eigenvalues \(\lambda_j\) of \(t^hA\) shall satisfy \(1+(\lambda_j')^2/(16\lambda_j^3)\neq 0\) on \((a,\infty]\). Under a modified eigenvalue condition the result is valid in the case that \(A(t)\) is meromorphic at \(t=\infty\) and not invertible there.