I am to prove that P_n(-x)=(-1)^n*P_n(x)
And, P'_n(-x)=(-1)^(n+1)*P'_n(x)
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?