Discuss the eigenfunctions of the sturm-liouville problem

Question

Assignment:

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer.

Expand ƒ(x) = H(x), on -1 < x < 1, in terms of the eigenfunctions of the Sturm-Liouville problem.

(1-x²)y" - 2xy' + λy = 0,

Where y(-1) and y(1) are bounded. Plot both ƒ(x) and the sum of the first four nonvanising terms of that expansion.