function[I11Lower, I11ttLower, I11xxLower, I11xtLower, I11txLower, I11x1Lower, I11x2Lower, I11t1Lower, I11t2Lower]=IDataTable11ULower (x1, x2, t1, t2, mR, mL, kappa)
I11Lower=@(omega,t)omega.^(-1).*(mL.^2+omega.^2).^(-1).*pi.^(-1).*cos(omega.*(t1+(-1) ...
  .*t2)).*coth(kappa.^(-1).*omega.*pi).*((mL.^2+omega.^2).*cos(( ...
  mL.^2+omega.^2).^(1/2).*xstar1).*cos((mL.^2+omega.^2).^(1/2).* ...
  xstar2)+omega.^2.*sin((mL.^2+omega.^2).^(1/2).*xstar1).*sin(( ...
  mL.^2+omega.^2).^(1/2).*xstar2));

I11ttLower=@(omega,t)omega.*(mL.^2+omega.^2).^(-1).*pi.^(-1).*cos(omega.*(t1+(-1).*t2)) ...
  .*coth(kappa.^(-1).*omega.*pi).*((mL.^2+omega.^2).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar1).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+ ...
  omega.^2.*sin((mL.^2+omega.^2).^(1/2).*xstar1).*sin((mL.^2+ ...
  omega.^2).^(1/2).*xstar2));

I11xxLower=@(omega,t)omega.^(-1).*pi.^(-1).*cos(omega.*(t1+(-1).*t2)).*coth(kappa.^(-1) ...
  .*omega.*pi).*(omega.^2.*cos((mL.^2+omega.^2).^(1/2).*(xstar1+(-1) ...
  .*xstar2))+mL.^2.*sin((mL.^2+omega.^2).^(1/2).*xstar1).*sin(( ...
  mL.^2+omega.^2).^(1/2).*xstar2));

I11xtLower=@(omega,t)(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*coth(kappa.^(-1).*omega.*pi).* ...
  sin(omega.*(t1+(-1).*t2)).*((-1).*(mL.^2+omega.^2).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2).*sin((mL.^2+omega.^2).^(1/2).*xstar1)+ ...
  omega.^2.*cos((mL.^2+omega.^2).^(1/2).*xstar1).*sin((mL.^2+ ...
  omega.^2).^(1/2).*xstar2));

I11txLower=@(omega,t)(1/2).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*coth(kappa.^(-1).* ...
  omega.*pi).*sin(omega.*(t1+(-1).*t2)).*((-1).*(mL.^2+2.*omega.^2) ...
  .*sin((mL.^2+omega.^2).^(1/2).*(xstar1+(-1).*xstar2))+mL.^2.*sin(( ...
  mL.^2+omega.^2).^(1/2).*(xstar1+xstar2)));

I11x1Lower=@(omega,t)omega.^(-1).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*cos(omega.*(t1+( ...
  -1).*t2)).*coth(kappa.^(-1).*omega.*pi).*((-1).*(mL.^2+omega.^2).* ...
  cos((mL.^2+omega.^2).^(1/2).*xstar2).*sin((mL.^2+omega.^2).^(1/2) ...
  .*xstar1)+omega.^2.*cos((mL.^2+omega.^2).^(1/2).*xstar1).*sin(( ...
  mL.^2+omega.^2).^(1/2).*xstar2));

I11x2Lower=@(omega,t)omega.^(-1).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*cos(omega.*(t1+( ...
  -1).*t2)).*coth(kappa.^(-1).*omega.*pi).*(omega.^2.*sin((mL.^2+ ...
  omega.^2).^(1/2).*(xstar1+(-1).*xstar2))+(-1).*mL.^2.*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar1).*sin((mL.^2+omega.^2).^(1/2).*xstar2)); ...
  

I11t1Lower=@(omega,t)(-1).*(mL.^2+omega.^2).^(-1).*pi.^(-1).*coth(kappa.^(-1).*omega.* ...
  pi).*sin(omega.*(t1+(-1).*t2)).*((mL.^2+omega.^2).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar1).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+ ...
  omega.^2.*sin((mL.^2+omega.^2).^(1/2).*xstar1).*sin((mL.^2+ ...
  omega.^2).^(1/2).*xstar2));

I11t2Lower=@(omega,t)(mL.^2+omega.^2).^(-1).*pi.^(-1).*coth(kappa.^(-1).*omega.*pi).* ...
  sin(omega.*(t1+(-1).*t2)).*((mL.^2+omega.^2).*cos((mL.^2+omega.^2) ...
  .^(1/2).*xstar1).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+omega.^2.* ...
  sin((mL.^2+omega.^2).^(1/2).*xstar1).*sin((mL.^2+omega.^2).^(1/2) ...
  .*xstar2));
