function f=chi_doppler(beta,x)
% Doppler chi function
   u=[ 3.43615913, 2.53273177, 1.75668371, 1.03661084, 0.342901319, ...
   -0.342901319, -1.03661084, -1.75668371, -2.53273177, -3.43615913 ] ;
   w=[ 7.64043307e-6, 0.00134364574, 0.0338743962, 0.240138605, 0.610862613, ...
   0.610862613, 0.240138605, 0.0338743962, 0.00134364574, 7.64043307e-6 ] ;
   f=0 ;
   for i=1:10
      aaa=1.0./(sqrt(pi)*(1+x.^2+2.*x.*beta.*u(i)+(beta.*u(i)).^2)) ;
      f=f+w(i).*aaa.*(x+u(i).*beta) ;
   end