Approximation of analytic functions by Kummer functions (Q978467)

In this interesting paper, the solution of the inhomogeneous Kummer differential equation, namely, the equation of the form \[ xy''+(\beta-x)y'-\alpha y=\sum_{m=0}^{\infty}a_mx^m, \] is given in terms of a series. The author applies this result to the proof of a local Hyers-Ulam stability of the Kummer differential equation in a special class of analytic functions. The results are illustrated by an example presented at the end of the paper.