Q4Advanced Engineering Mathematics II

Question

Establish the following result for orthogonality of Legendre Polynomial $\int_{- 1}^{1} P_{m} (x) P_{n} (x) d x = 0, if m \neq = n .$

Answer 1

Question

10 marks

Establish the following result for orthogonality of Legendre Polynomial $\int_{- 1}^{1} P_{m} (x) P_{n} (x) d x = 0, if m \neq = n .$

Answer

Orthogonality of Legendre polynomials (integral of Pm*Pn from -1 to 1 = 0 for m != n) is established by showing Pm and Pn satisfy Legendre's equation and using Green's identity (Sturm-Liouville theory).