8. (generating function for Bessel function): Just as there is a generating function for the Legendre polynomials, there is one for the Bessel functions. Specifically, it can be show that: J, (X) : " 71=-00 Use generating function to derive various properties Bessel's function: (a): d J. ( X) = n-1 (X) -J.(X)) (hint take of both sides) dx (b): X Jn+1(X) = (Jn(X) + Jn+2(X)) (hint: take of both sides) 2(n +1) at