function [u_12r, u_12theta, u_3r, u_3theta, u_incr, u_inctheta] = depl(n,r)
global kp_a kp_b ks_a ks_b 

u_12r =[kp_b*(-besselh(n+1,1,kp_b*r)+ n/(kp_b*r)*besselh(n,1,kp_b*r)), n/r*besselh(n,1,ks_b*r), kp_b*(besselh(n-1,2,kp_b*r)-n/(kp_b*r)*besselh(n,2,kp_b*r)), n/r*besselh(n,2,ks_b*r)];
u_12theta = [-n/r*besselh(n,1,kp_b*r), -ks_b*(-besselh(n+1,1,ks_b*r)+n/(ks_b*r)*besselh(n,1,ks_b*r)), -n/r*besselh(n,2,kp_b*r), -ks_b*(besselh(n-1,2,ks_b*r)-n/(ks_b*r)*besselh(n,2,ks_b*r))];
u_3r = [kp_a*(-besselj(n+1,kp_a*r)+n/(kp_a*r)*besselj(n,kp_a*r)), n/r*besselj(n,ks_a*r)];
u_3theta = [-n/r*besselj(n,kp_a*r), -ks_a*(-besselj(n+1,ks_a*r)+n/(ks_a*r)*besselj(n,ks_a*r))];
u_incr = epsilon(n)*1i**n*kp_b*(-besselj(n+1,kp_b*r)+n/(kp_b*r)*besselj(n,kp_b*r));
u_inctheta = -n/r*epsilon(n)*1i**n*besselj(n,kp_b*r);

endfunction


function epsilon = epsilon(n)
  if n==0
    epsilon = 1;
  else
    epsilon = 2;
  end
endfunction  