The Mathieu functions MathieuC(a, q, x) and MathieuS(a, q, x) are solutions of the Mathieu differential equation. MathieuC and MathieuS are even and odd functions of x, respectively. MathieuFloquet(a, q, x) is a Floquet solution of Mathieu's equation. where nu = MathieuExponent(a, q) is the characteristic exponent and P(x) is a Pi periodic function.
We present a few plots to demonstrate the usefullness of these functions below. This report has treated, in some detail, the mathematics behind the ideal rf Paul trap. Of course, the actual realization of the trap differs in many important ways from its ideal, but we may approach these realizations, in their many forms, with a fundamental understanding of their operational basis.