Mathieu functions of general order: connection formulae, base functions and asymptotic formulae. I. Introduction

Abstract
This is the first, introductory, paper of a series devoted to the derivation of a comprehensive set of approximate formulae for solutions of Mathieu’s equation with real parameters, in terms both of elementary and of higher transcendental functions. Order-of-magnitude error-estimates are obtained; these in every case reflect faithfully the behaviour of the actual error over the appropriate range of parameters and of independent variable. The general scope of the work is outlined in this Introduction, and is compared with that of previous work, in particular that of Langer (1934 b ). There then follows a description of the plan of the work and of the content of the several parts.

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