Let \(f(x)\) be a function such that \((1-x^2) f”(x) – 2x f'(x) + \alpha (\alpha+1) f(x) =0\)
for some \(\alpha \not\in \mathbb{N}\). Define \(P_n (x) = \frac{d^n}{dx^n} (x^2-1)^n\) for \(n =0,1,…\). Compute \(\int_{-1}^1 f(x) P_n(x) dx.\)

The best solution was submitted by 정서윤 (수리과학과 23학번, +4). Congratulations!

Here is the best solution of problem 2026-06.

Other solutions were submitted by 김은성 (서울대 수리과학부, +3), 신민규 (수리과학과 24학번, +3), 이상주 (경남대 수학교육과, +3), 장현준 (서울과학고 3학년, +3), 지은성 (수리과학과 석박통합과정, +3), Huseyn Ismayilov (전산학부 22학번, +3).