Unique summing of formal power series solutions to advanced and delayed differential equations (Q934477)

From the authors' abstract: The analytic delayed differential equation \[ z^2\psi'(z)+\psi(z/q)=z \] for \(q>1\) has a solution which can be expressed as a formal power series. A \(q\)-advanced Laplace-Borel kernel provides for the construction of an analytic solution whose domain is the right half plane with vertex at the initial point \(z=0\). This method is extended to provide a continuous family of solutions, of which a subfamily extends to a punctured neighborhood of \(z=0\) on the logarithmic Riemann surface. Conditions are given on the asymptotics of \(\psi'(z)\) near \(z=0\) to ensure uniqueness.