function[I31LRLower, I31LRttLower, I31LRxxLower, I31LRxtLower, I31LRtxLower, I31LRx1Lower, I31LRx2Lower, I31LRt1Lower, I31LRt2Lower]=IDataTable31LRULower (x1, x2, t1, t2, mR, mL, kappa)
I31LRLower=@(omega,t)(-1).*mR.^(-2).*omega.^(-1).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).* ...
  csch(kappa.^(-1).*omega.*pi).*(omega.*cos(omega.*(t1+(-1).*t2)).*( ...
  sin(omega.*xstar1).*(((mR+(-1).*omega).*(mR+omega).*(mL.^2+ ...
  omega.^2)).^(1/2).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+((-1).*mR+ ...
  omega).*(mR+omega).*sin((mL.^2+omega.^2).^(1/2).*xstar2))+omega.* ...
  cos(omega.*xstar1).*((-1).*(mL.^2+omega.^2).^(1/2).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)+((mR+(-1).*omega).*(mR+omega)).^(1/2).* ...
  sin((mL.^2+omega.^2).^(1/2).*xstar2)))+sin(omega.*(t1+(-1).*t2)).* ...
  (omega.*cos(omega.*xstar1).*(((mR+(-1).*omega).*(mR+omega).*( ...
  mL.^2+omega.^2)).^(1/2).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+ ...
  omega.^2.*sin((mL.^2+omega.^2).^(1/2).*xstar2))+sin(omega.*xstar1) ...
  .*((mL.^2+omega.^2).^(1/2).*((-1).*mR.^2+omega.^2).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)+(-1).*omega.^2.*((mR+(-1).*omega).*(mR+ ...
  omega)).^(1/2).*sin((mL.^2+omega.^2).^(1/2).*xstar2))));

I31LRttLower=@(omega,t)(1/2).*mR.^(-2).*omega.*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch( ...
  kappa.^(-1).*omega.*pi).*(mR.^2.*(mL.^2+omega.^2).^(1/2).*cos( ...
  omega.*(t1+(-1).*t2+(-1).*xstar1)).*cos((mL.^2+omega.^2).^(1/2).* ...
  xstar2)+(-2).*omega.*((mR+(-1).*omega).*(mR+omega).*(mL.^2+ ...
  omega.^2)).^(1/2).*cos((mL.^2+omega.^2).^(1/2).*xstar2).*sin( ...
  omega.*(t1+(-1).*t2+xstar1))+(-1).*mR.^2.*omega.*sin(omega.*(t1+( ...
  -1).*t2+(-1).*xstar1)).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+ ...
  mR.^2.*omega.*sin(omega.*(t1+(-1).*t2+xstar1)).*sin((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)+(-2).*omega.^3.*sin(omega.*(t1+(-1).*t2+ ...
  xstar1)).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+cos(omega.*(t1+(-1) ...
  .*t2+xstar1)).*((mL.^2+omega.^2).^(1/2).*((-1).*mR.^2+2.*omega.^2) ...
  .*cos((mL.^2+omega.^2).^(1/2).*xstar2)+(-2).*omega.^2.*((mR+(-1).* ...
  omega).*(mR+omega)).^(1/2).*sin((mL.^2+omega.^2).^(1/2).*xstar2))) ...
  ;

I31LRxxLower=@(omega,t)(1/2).*mR.^(-2).*pi.^(-1).*csch(kappa.^(-1).*omega.*pi).*(mR.^2.* ...
  omega.*cos(omega.*(t1+(-1).*t2+(-1).*xstar1)).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)+(-1).*mR.^2.*(mL.^2+omega.^2).^(1/2).* ...
  sin(omega.*(t1+(-1).*t2+(-1).*xstar1)).*sin((mL.^2+omega.^2).^( ...
  1/2).*xstar2)+omega.*cos(omega.*(t1+(-1).*t2+xstar1)).*((mR.^2+( ...
  -2).*omega.^2).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+2.*((mR+(-1) ...
  .*omega).*(mR+omega).*(mL.^2+omega.^2)).^(1/2).*sin((mL.^2+ ...
  omega.^2).^(1/2).*xstar2))+sin(omega.*(t1+(-1).*t2+xstar1)).*(2.* ...
  omega.^2.*((mR+(-1).*omega).*(mR+omega)).^(1/2).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)+(mL.^2+omega.^2).^(1/2).*((-1).*mR.^2+ ...
  2.*omega.^2).*sin((mL.^2+omega.^2).^(1/2).*xstar2)));

I31LRxtLower=@(omega,t)(1/2).*mR.^(-2).*omega.*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch( ...
  kappa.^(-1).*omega.*pi).*((-1).*mR.^2.*(mL.^2+omega.^2).^(1/2).* ...
  cos(omega.*(t1+(-1).*t2+(-1).*xstar1)).*cos((mL.^2+omega.^2).^( ...
  1/2).*xstar2)+(-2).*omega.*((mR+(-1).*omega).*(mR+omega).*(mL.^2+ ...
  omega.^2)).^(1/2).*cos((mL.^2+omega.^2).^(1/2).*xstar2).*sin( ...
  omega.*(t1+(-1).*t2+xstar1))+(-2).*omega.^3.*sin(omega.*(t1+(-1).* ...
  t2+xstar1)).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+mR.^2.*omega.*( ...
  sin(omega.*(t1+(-1).*t2+(-1).*xstar1))+sin(omega.*(t1+(-1).*t2+ ...
  xstar1))).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+cos(omega.*(t1+( ...
  -1).*t2+xstar1)).*((mL.^2+omega.^2).^(1/2).*((-1).*mR.^2+2.* ...
  omega.^2).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+(-2).*omega.^2.*(( ...
  mR+(-1).*omega).*(mR+omega)).^(1/2).*sin((mL.^2+omega.^2).^(1/2).* ...
  xstar2)));

I31LRtxLower=@(omega,t)(1/2).*mR.^(-2).*pi.^(-1).*csch(kappa.^(-1).*omega.*pi).*((-1).* ...
  mR.^2.*omega.*cos(omega.*(t1+(-1).*t2+(-1).*xstar1)).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)+mR.^2.*(mL.^2+omega.^2).^(1/2).*sin( ...
  omega.*(t1+(-1).*t2+(-1).*xstar1)).*sin((mL.^2+omega.^2).^(1/2).* ...
  xstar2)+omega.*cos(omega.*(t1+(-1).*t2+xstar1)).*((mR.^2+(-2).* ...
  omega.^2).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+2.*((mR+(-1).* ...
  omega).*(mR+omega).*(mL.^2+omega.^2)).^(1/2).*sin((mL.^2+omega.^2) ...
  .^(1/2).*xstar2))+sin(omega.*(t1+(-1).*t2+xstar1)).*(2.*omega.^2.* ...
  ((mR+(-1).*omega).*(mR+omega)).^(1/2).*cos((mL.^2+omega.^2).^(1/2) ...
  .*xstar2)+(mL.^2+omega.^2).^(1/2).*((-1).*mR.^2+2.*omega.^2).*sin( ...
  (mL.^2+omega.^2).^(1/2).*xstar2)));

I31LRx1Lower=@(omega,t)(1/2).*mR.^(-2).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch(kappa.^( ...
  -1).*omega.*pi).*((mL.^2+omega.^2).^(1/2).*cos((mL.^2+omega.^2).^( ...
  1/2).*xstar2).*(mR.^2.*sin(omega.*(t1+(-1).*t2+(-1).*xstar1))+( ...
  mR.^2+(-2).*omega.^2).*sin(omega.*(t1+(-1).*t2+xstar1)))+omega.*( ...
  mR.^2.*cos(omega.*(t1+(-1).*t2+(-1).*xstar1))+2.*omega.*((mR+(-1) ...
  .*omega).*(mR+omega)).^(1/2).*sin(omega.*(t1+(-1).*t2+xstar1))).* ...
  sin((mL.^2+omega.^2).^(1/2).*xstar2)+omega.*cos(omega.*(t1+(-1).* ...
  t2+xstar1)).*((-2).*((mR+(-1).*omega).*(mR+omega).*(mL.^2+ ...
  omega.^2)).^(1/2).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+(mR.^2+( ...
  -2).*omega.^2).*sin((mL.^2+omega.^2).^(1/2).*xstar2)));

I31LRx2Lower=@(omega,t)mR.^(-2).*omega.^(-1).*pi.^(-1).*csch(kappa.^(-1).*omega.*pi).*( ...
  omega.^2.*cos((mL.^2+omega.^2).^(1/2).*xstar2).*(((mR+(-1).*omega) ...
  .*(mR+omega)).^(1/2).*sin(omega.*(t1+(-1).*t2)).*sin(omega.* ...
  xstar1)+(-1).*omega.*sin(omega.*(t1+(-1).*t2+xstar1)))+sin(omega.* ...
  (t1+(-1).*t2)).*(omega.*((mR+(-1).*omega).*(mR+omega).*(mL.^2+ ...
  omega.^2)).^(1/2).*cos(omega.*xstar1)+(mL.^2+omega.^2).^(1/2).*(( ...
  -1).*mR.^2+omega.^2).*sin(omega.*xstar1)).*sin((mL.^2+omega.^2).^( ...
  1/2).*xstar2)+omega.*cos(omega.*(t1+(-1).*t2)).*((-1).*omega.*cos( ...
  omega.*xstar1).*(((mR+(-1).*omega).*(mR+omega)).^(1/2).*cos(( ...
  mL.^2+omega.^2).^(1/2).*xstar2)+(mL.^2+omega.^2).^(1/2).*sin(( ...
  mL.^2+omega.^2).^(1/2).*xstar2))+sin(omega.*xstar1).*(mR.^2.*cos(( ...
  mL.^2+omega.^2).^(1/2).*xstar2)+((mR+(-1).*omega).*(mR+omega).*( ...
  mL.^2+omega.^2)).^(1/2).*sin((mL.^2+omega.^2).^(1/2).*xstar2)))); ...
  

I31LRt1Lower=@(omega,t)(-1/2).*mR.^(-2).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch( ...
  kappa.^(-1).*omega.*pi).*((mL.^2+omega.^2).^(1/2).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2).*(mR.^2.*sin(omega.*(t1+(-1).*t2+(-1).* ...
  xstar1))+(-1).*(mR.^2+(-2).*omega.^2).*sin(omega.*(t1+(-1).*t2+ ...
  xstar1)))+omega.*(mR.^2.*cos(omega.*(t1+(-1).*t2+(-1).*xstar1))+( ...
  -2).*omega.*((mR+(-1).*omega).*(mR+omega)).^(1/2).*sin(omega.*(t1+ ...
  (-1).*t2+xstar1))).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+omega.* ...
  cos(omega.*(t1+(-1).*t2+xstar1)).*(2.*((mR+(-1).*omega).*(mR+ ...
  omega).*(mL.^2+omega.^2)).^(1/2).*cos((mL.^2+omega.^2).^(1/2).* ...
  xstar2)+(-1).*(mR.^2+(-2).*omega.^2).*sin((mL.^2+omega.^2).^(1/2) ...
  .*xstar2)));

I31LRt2Lower=@(omega,t)(1/2).*mR.^(-2).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch(kappa.^( ...
  -1).*omega.*pi).*((mL.^2+omega.^2).^(1/2).*cos((mL.^2+omega.^2).^( ...
  1/2).*xstar2).*(mR.^2.*sin(omega.*(t1+(-1).*t2+(-1).*xstar1))+(-1) ...
  .*(mR.^2+(-2).*omega.^2).*sin(omega.*(t1+(-1).*t2+xstar1)))+ ...
  omega.*(mR.^2.*cos(omega.*(t1+(-1).*t2+(-1).*xstar1))+(-2).* ...
  omega.*((mR+(-1).*omega).*(mR+omega)).^(1/2).*sin(omega.*(t1+(-1) ...
  .*t2+xstar1))).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+omega.*cos( ...
  omega.*(t1+(-1).*t2+xstar1)).*(2.*((mR+(-1).*omega).*(mR+omega).*( ...
  mL.^2+omega.^2)).^(1/2).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+(-1) ...
  .*(mR.^2+(-2).*omega.^2).*sin((mL.^2+omega.^2).^(1/2).*xstar2))); ...
  
