Ortogonality conditions The Legendre polynomials and functions are orthogonal P()P(t)dt=2 2n+1 Pim(t)pm(t)dt 2(n+m)! 2n+1(n-m) nn 02/1302 12.540Lec0302/13/02 12.540 Lec 03 10 Ortogonality conditions • The Legendre polynomials and functions are orthogonal: Pn' ( t ) −1 1 ∫ Pn ( t )dt = 2 2 n + 1 δ n'n Pn'm ( t ) −1 1 ∫ Pnm ( t )dt = 2 2 n + 1 ( n + m)! ( n − m)! δ n'n