We consider the case where $I = [-1,1]$ and $w(x) = 1$. Let $(p_n)_{n \in \mathbb{N}}$ be the sequence of orthogonal polynomials associated with the weight $w$ (monic, $\deg(p_n) = n$, orthogonal for $\langle f, g \rangle = \int_{-1}^1 f(x)g(x)\,\mathrm{d}x$).
Determine the first four orthogonal polynomials $(p_0, p_1, p_2, p_3)$ associated with the weight $w$.