Question 5 (a) Use the Rodrigues' formula to find the Legendre polynomials Po(x), P:(x), P2(x), P3(x). Show your calculation explicitly. (b) Find the first three Fourier-Legendre coefficients co, C1,...

Extracted text: Question 5 (a) Use the Rodrigues' formula to find the Legendre polynomials Po(x), P:(x), P2(x), P3(x). Show your calculation explicitly. (b) Find the first three Fourier-Legendre coefficients co, C1, C2 for the function f (x) = cos Show your calculation explicitly. (c) The Bessel function J1 (x) can be expressed in terms of basic functions (for example the functions sin r and below) and constants, JĄ (2) = sin x. Use the recurrence relations of Bessel functions to find J3 (x) and express it in terms of basic functions. 一2