Answer Happy

Hello, kindly I need the solution with the full detailed steps for the attached question. The answer to be using the method mentioned in the hint and question.
This is an advanced mathematical problem. So, please don't solve it according to physics laws like electromagnetic theory,
Problem 8: In electromagnetic scattering by an infinite cylinder of radius a, under certain conditions, the time-harmonic electric field is given by E = u(0,0)2, where u satisfies the Helmholtz wave equation 0 < p <a, 0 < 0 < 27 32 1 Әи 1 02 + + apa tp de +2?u= 0, др2 р др p2 862 u(0,6) is finite, u(a, b) = eika cos u(0,0) = u(p,27), up(0,0) = u$(p, 27) where k is a constant. Solve it. Hint: Use the generating function of the Bessel function when obtaining the unknown coefficient.