We consider the Sturm–Liouville equation\renewcommand{\theequation}{1.\arabic{equation}}\begin{equation}y^{\prime\prime}(x)+\{\lambda - q(x)\}y(x) = 0\quad (0 \le x < \infty)\end{equation}with a boundary condition at $x = 0$ which can be either the Dirichlet condition\begin{equation}y(0) = 0\end{equation}or the Neumann condition\begin{equation}y^\prime(0) = 0.\end{equation}As usual, $\lambda$ is the complex spectral parameter with $0 \le \arg \lambda < 2\pi$, and the potential $q$ is real-valued and locally integrable in $[0, \infty)$.