The Ince equation,
d^2F/dz^2 + q*sin(2z)dF/dz+(\eta p*q*cos(2z))*F=0,

is a periodic linear second-order differential equation that has two families of independent solutions: the even C^{m}_p(z,q) and odd S^{m}_p(z,q) Ince polynomials of order p and degree m, and parameter q. These functions calculate the Ince polynomials.

For more information about Ince Polynomial:

Miguel A. Bandres and Julio C. Gutiérrez-Vega, "Ince-Gaussian modes of the paraxial wave equation and stable resonators"
Journal of the Optical Society of America A, 21(5), 873-880 (2004)
( http://goo.gl/rqq7nQ )