function[I31Lower, I31ttLower, I31xxLower, I31xtLower, I31txLower, I31x1Lower, I31x2Lower, I31t1Lower, I31t2Lower]=IDataTable31ULower (x1, x2, t1, t2, mR, mL, kappa)
I31Lower=@(omega,t)(1/4).*mR.^(-2).*omega.^(-1).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).* ...
  csch(kappa.^(-1).*omega.*pi).^2.*(mR.^2.*(mL.^2+omega.^2).^(1/2).* ...
  cos(omega.*(t1+(-1).*t2+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+(-1).*xstar1))+omega.*((-1).*(mR.^2+(-2).*omega.^2).*sin( ...
  omega.*(t1+(-1).*t2+(-1).*xstar1))+mR.^2.*sin(omega.*(t1+(-1).*t2+ ...
  xstar1))).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+cos(omega.*(t1+( ...
  -1).*t2+(-1).*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))).*sinh(2.*kappa.^(-1).*omega.*pi);

I31ttLower=@(omega,t)(1/4).*mR.^(-2).*omega.*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch( ...
  kappa.^(-1).*omega.*pi).^2.*(mR.^2.*(mL.^2+omega.^2).^(1/2).*cos( ...
  omega.*(t1+(-1).*t2+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+( ...
  -1).*xstar1))+omega.*((-1).*(mR.^2+(-2).*omega.^2).*sin(omega.*( ...
  t1+(-1).*t2+(-1).*xstar1))+mR.^2.*sin(omega.*(t1+(-1).*t2+xstar1)) ...
  ).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+cos(omega.*(t1+(-1).*t2+( ...
  -1).*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))) ...
  .*sinh(2.*kappa.^(-1).*omega.*pi);

I31xxLower=@(omega,t)(1/4).*mR.^(-2).*pi.^(-1).*csch(kappa.^(-1).*omega.*pi).^2.*( ...
  omega.*((mR.^2+(-2).*omega.^2).*cos(omega.*(t1+(-1).*t2+(-1).* ...
  xstar1))+mR.^2.*cos(omega.*(t1+(-1).*t2+xstar1))).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)+(-2).*omega.^2.*((mR+(-1).*omega).*(mR+ ...
  omega)).^(1/2).*cos((mL.^2+omega.^2).^(1/2).*xstar2).*sin(omega.*( ...
  t1+(-1).*t2+(-1).*xstar1))+2.*omega.*((mR+(-1).*omega).*(mR+omega) ...
  .*(mL.^2+omega.^2)).^(1/2).*cos(omega.*(t1+(-1).*t2+(-1).*xstar1)) ...
  .*sin((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)+(-2).*omega.^2.*(mL.^2+omega.^2).^(1/2).*sin( ...
  omega.*(t1+(-1).*t2+(-1).*xstar1)).*sin((mL.^2+omega.^2).^(1/2).* ...
  xstar2)+mR.^2.*(mL.^2+omega.^2).^(1/2).*sin(omega.*(t1+(-1).*t2+ ...
  xstar1)).*sin((mL.^2+omega.^2).^(1/2).*xstar2)).*sinh(2.*kappa.^( ...
  -1).*omega.*pi);

I31xtLower=@(omega,t)(1/4).*mR.^(-2).*omega.*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch( ...
  kappa.^(-1).*omega.*pi).^2.*(mR.^2.*(mL.^2+omega.^2).^(1/2).*cos( ...
  omega.*(t1+(-1).*t2+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+(-1).*xstar1))+omega.*((mR.^2+(-2).*omega.^2).*sin(omega.*(t1+( ...
  -1).*t2+(-1).*xstar1))+mR.^2.*sin(omega.*(t1+(-1).*t2+xstar1))).* ...
  sin((mL.^2+omega.^2).^(1/2).*xstar2)+cos(omega.*(t1+(-1).*t2+(-1) ...
  .*xstar1)).*((mR.^2+(-2).*omega.^2).*(mL.^2+omega.^2).^(1/2).*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))).*sinh( ...
  2.*kappa.^(-1).*omega.*pi);

I31txLower=@(omega,t)(1/4).*mR.^(-2).*pi.^(-1).*csch(kappa.^(-1).*omega.*pi).^2.*( ...
  omega.*((-1).*(mR.^2+(-2).*omega.^2).*cos(omega.*(t1+(-1).*t2+(-1) ...
  .*xstar1))+mR.^2.*cos(omega.*(t1+(-1).*t2+xstar1))).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)+2.*omega.^2.*((mR+(-1).*omega).*(mR+ ...
  omega)).^(1/2).*cos((mL.^2+omega.^2).^(1/2).*xstar2).*sin(omega.*( ...
  t1+(-1).*t2+(-1).*xstar1))+(-2).*omega.*((mR+(-1).*omega).*(mR+ ...
  omega).*(mL.^2+omega.^2)).^(1/2).*cos(omega.*(t1+(-1).*t2+(-1).* ...
  xstar1)).*sin((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)+2.*omega.^2.*(mL.^2+omega.^2) ...
  .^(1/2).*sin(omega.*(t1+(-1).*t2+(-1).*xstar1)).*sin((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)+mR.^2.*(mL.^2+omega.^2).^(1/2).*sin( ...
  omega.*(t1+(-1).*t2+xstar1)).*sin((mL.^2+omega.^2).^(1/2).*xstar2) ...
  ).*sinh(2.*kappa.^(-1).*omega.*pi);

I31x1Lower=@(omega,t)(1/4).*mR.^(-2).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch(kappa.^( ...
  -1).*omega.*pi).^2.*((mL.^2+omega.^2).^(1/2).*cos((mL.^2+omega.^2) ...
  .^(1/2).*xstar2).*((-1).*(mR.^2+(-2).*omega.^2).*sin(omega.*(t1+( ...
  -1).*t2+(-1).*xstar1))+(-1).*mR.^2.*sin(omega.*(t1+(-1).*t2+ ...
  xstar1)))+omega.*(mR.^2.*cos(omega.*(t1+(-1).*t2+xstar1))+(-2).* ...
  omega.*((mR+(-1).*omega).*(mR+omega)).^(1/2).*sin(omega.*(t1+(-1) ...
  .*t2+(-1).*xstar1))).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+omega.* ...
  cos(omega.*(t1+(-1).*t2+(-1).*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))).*sinh(2.*kappa.^(-1).*omega.*pi);

I31x2Lower=@(omega,t)(-1/4).*mR.^(-2).*omega.^(-1).*pi.^(-1).*csch(kappa.^(-1).*omega.* ...
  pi).^2.*(omega.*cos((mL.^2+omega.^2).^(1/2).*xstar2).*((mR.^2+(-2) ...
  .*omega.^2).*sin(omega.*(t1+(-1).*t2+(-1).*xstar1))+(-1).*mR.^2.* ...
  sin(omega.*(t1+(-1).*t2+xstar1)))+(mR.^2.*(mL.^2+omega.^2).^(1/2) ...
  .*cos(omega.*(t1+(-1).*t2+xstar1))+2.*omega.*((mR+(-1).*omega).*( ...
  mR+omega).*(mL.^2+omega.^2)).^(1/2).*sin(omega.*(t1+(-1).*t2+(-1) ...
  .*xstar1))).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+cos(omega.*(t1+( ...
  -1).*t2+(-1).*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))).*sinh(2.*kappa.^(-1).*omega.*pi);

I31t1Lower=@(omega,t)(1/4).*mR.^(-2).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch(kappa.^( ...
  -1).*omega.*pi).^2.*((-1).*(mL.^2+omega.^2).^(1/2).*cos((mL.^2+ ...
  omega.^2).^(1/2).*xstar2).*((-1).*(mR.^2+(-2).*omega.^2).*sin( ...
  omega.*(t1+(-1).*t2+(-1).*xstar1))+mR.^2.*sin(omega.*(t1+(-1).*t2+ ...
  xstar1)))+omega.*(mR.^2.*cos(omega.*(t1+(-1).*t2+xstar1))+2.* ...
  omega.*(mR.^2+(-1).*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+(-1).*xstar1)).*(2.*((mR.^2+(-1).*omega.^2).*( ...
  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))).* ...
  sinh(2.*kappa.^(-1).*omega.*pi);

I31t2Lower=@(omega,t)(1/4).*mR.^(-2).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch(kappa.^( ...
  -1).*omega.*pi).^2.*((mL.^2+omega.^2).^(1/2).*cos((mL.^2+omega.^2) ...
  .^(1/2).*xstar2).*((-1).*(mR.^2+(-2).*omega.^2).*sin(omega.*(t1+( ...
  -1).*t2+(-1).*xstar1))+mR.^2.*sin(omega.*(t1+(-1).*t2+xstar1)))+( ...
  -1).*omega.*(mR.^2.*cos(omega.*(t1+(-1).*t2+xstar1))+2.*omega.*(( ...
  mR+(-1).*omega).*(mR+omega)).^(1/2).*sin(omega.*(t1+(-1).*t2+(-1) ...
  .*xstar1))).*sin((mL.^2+omega.^2).^(1/2).*xstar2)+omega.*cos( ...
  omega.*(t1+(-1).*t2+(-1).*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))).*sinh(2.*kappa.^(-1).*omega.*pi);
