Question

p(x)x4 2x3 x2 2x1 as a sum of Legendre Polynomial

Answer 1

Answer:

a) −2x2+7

b) 3x4+6x2−2

c) cos5θ - the L.P. will be in functions of cosθ.

If anyone could help me understand the setup process for Legendres, that would be highly appreciated. I have no exposure to Legendre series, and I am using Griffith's Intro. to Electrodynamics which doesn't provide the explanation of Legendre series in any detail.

You may determine the coefficients in the series algebraically or using the orthogonality properties of the Legendre polynomials.

Edit: It seems that the solutions for Legendre polynomial are set, such as the values of P0, P1, P2, etc... But how do I incorporate the given function? Do I make them into a polynomial, then attempt to set that in series that is equal to the Legendre series? For (c), I am assuming to express that in complex terms.. The hint suggests to use orthogonality properties, in which the normalization would be 1?