TITLE: Theory of the Mathieu Operator
QUESTION [5 upvotes]: How important is the theory of the Mathieu operator in mathematics/applied mathematics? What are the major mathematical concepts required to study it?
The Mathieu operator is an ordinary periodic differential operator of the form
$$\frac{d^2y}{dx^2} + (a-2q \cos{2x})y =0.$$

REPLY [2 votes]: For better understanding of Mathieu functions I recommend a classical book by M. Abramovitz and I. Stegun and Mathieu Functions Toolbox implemented in Scilab.