Holomorphic Regularization of Singularly Perturbed Integro-Differential Equations

S.A. Lomov’s regularization method has long been used to solve integro-differentialsingularly perturbed equations, which are very important from the viewpoint of applications. Inthis method, the series in powers of a small parameter representing the solutions of theseequations converge asymptotically. However, in accordance with the main concept of the method,to construct a general singular perturbation theory one must indicate conditions for the ordinaryconvergence of these series. This is the subject of the present paper.