(a) We can write , we have
Therefore,
which is of the form in question (name coefficients as )
We can do this repeatedly, for , then , et cetera, to get
(b) Since , we have
Using part a) above, this becomes a linear combination of the polynomials . Let us write
Then
Since the Legendre polynomials are orthogonal, each of the integrals above is zero. Hence,
Pleasehelpmewiththisproblem! Thanks! 10. (a) By recalling that Pm(x) is a polynomial of degree m containing only the powers r", Х'n-2, X,"-4, . . . of x (Sec. 99), state why where the...