Use the generating function for the Bessel functions, N /H g (x , t ) = e =EJn(alt to obtain the following recurrence relations: 2n a) Just Jn+ = b) Jn-1 - Jn+1 = 2J.', c) Jn- 1 - - Jn = Jn d) Jnt1 - - Jn = - Jn e) Using the above results verify that Jr satisfies Bessel's equation, a' J," + a J,'t (x2 - n?) J, =0. f) Verify that the series solution n +2s (-1). In (x ) = E N/8 s=0 s !(n + s)! satisfies the same equation