Ince equation

In mathematics, the Ince equation, named for Edward Lindsay Ince, is the differential equation


 * $$w^{\prime\prime}+\xi\sin(2z)w^{\prime}+(\eta-p\xi\cos(2z))w=0. \, $$

When p is a non-negative integer, it has polynomial solutions called Ince polynomials. In particular, when $$p=1, \eta\pm\xi=1$$, then it has a closed-form solution

$$w(z)=Ce^{-iz}(e^{2iz}\mp 1)$$

where $$C$$ is a constant.