In previous papers, we have started to develop a fully effective complex analysis. The aim of this theory is to evaluate constructible analytic functions to any desired precision and to continue such functions analytically whenever possible. In order to guarantee that the desired precision is indeed obtained, bound computations are an important part of this program. In this paper we will recall or show how the classical majorant technique can be used in order to obtain many such bounds.

Keywords: majorant equations, power series, computer algebra, partial differential equations, singular differential equations, convolution products

A.M.S. subject classification: 35A10, 13F25, 44A35

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