I am reading about the eigenvalue problem
$$-\frac{d^2}{dx^2}u = \lambda u$$
with periodic boundary conditions.
This article (equation 12b) implies the eigenfunctions have the forms
$$u(x) = 1\\ u(x) = A\cos(n\pi x/L)\\u(x) = A\sin(n\pi x/L)$$
However, I thought the correct form was
$$u(x) = Ae^{i n\pi x/L}$$
Are these two forms related or somehow equivalent?