1. The problem statement, all variables and given/known data I am to prove that P_n(-x)=(-1)^n*P_n(x) And, P'_n(-x)=(-1)^(n+1)*P'_n(x) 2. Relevant equations 3. The attempt at a solution I know that whether a Legendre Polynomial is an even or odd function depends on its degree.It follows directly from the solution of Legendre differential equation.But,to prove these properties I am getting stuck. Can anyone help me to start with these?