LP.27 LP Exercises 25 and 26 combine to give the orthogonality and normalization condition for the Legendre polynomials, IP eqn 34: Completeness tells us we can rewrite any (sufficiently nice) function / () as a sum of coefficients times Legendre polynomials: s (x) = [ an Pu(I). Last, we will also need the definition of the "scalar product" with a Legendre polynomial from the OFFS tutorial: ( . P. ) = [ f(x) Pr(x) d. Using these three equations, find an expression for On in terms of the scalar product: 2n+ 1 * (f, P.). Then, rewrite each of the following entirely in terms of sums of Legendre polynomials (note *every* summand in your expressions must contain one Legendre polynomial). For entry tips, see the hints below. 1 = X 4 X = Po ( * ) + = p , ( x ) X + Pa (x) X X Note: 76"F