Notes on the zeros of the solutions of the non-homogeneous Airy's equation

Abstract

We present some observations on the distribution of the zeros of solutions of the nonhomogeneous Airy's equation. We show the existence of a principal family of solutions, with simple zeros, and particular solutions, characterized by a double zero in a given position of the complex plane. A recursion, describing the distribution of the zeros, is introduced and the limits of its applicability are discussed. The results can be considered a generalization of previous works on the distribution of the zeros for the solutions of the corresponding homogeneous equation

Submitted to FASNET (Formal and Analytic Solutions of Differential Equations), Proceedings of the webconference FASNET organized in Alcala, Spain, June 29th to 30th 2020