LP Exercises 25 and 26 combine to give the orthogonality and normalization condition for the Legendre polynomials, LP eqn 34: Pm(x) Pr(x) dx = 2n+ 1 2 Tomn. Completeness tells us we can rewrite any (sufficiently nice) function J () as a sum of coefficients times Legendre polynomials: f (x) = [ an Pr(x). Last, we will also need the definition of the "scalar product" with a Legendre polynomial from the OFFS tutorial: ( f . P.. ) = [ f(x) Pr(x) dx. Using these three equations, find an expression for On in terms of the scalar product: an (2n + 1) * (f , Pr). 2 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 2-3