For an even weight function prove that the orthogonal polynomial is even or odd function depending on the grade.

Let $$w(x)$$ be an even weight function and [a,b] is a symmetric region with respect to $$0$$. Prove that the orthogonal polynomial satisfies $$p_{n}(-x)=(-1)^{n}p_{n}(x)$$ for $$n=0,1,2..$$

It says that an orthogonal polynomial with respect to an even weight function, is even or odd function depending on its grade.