fHR4=1/(Sqrt[4*Pi*omega])*2*omega/(omega+kR)* Exp[-I*omega*t]*Exp[I*kR*xstar];
fHR3=1/(Sqrt[4*Pi*omega])*Exp[-I*omega*t]*(Exp[I*omega*xstar]+(omega-kR)/(omega+kR)*Exp[-I*omega*xstar]);
fHR2=1/(Sqrt[4*Pi*omega])*((omega-kR)/(omega+kR))*Exp[-I*omega*t]*Exp[-I*omega*xstar];
fHR1 =1/(Sqrt[4*Pi*omega])*((omega-kR)/(omega+kR))*Exp[-I*omega*t]*((kL+omega)/(2*kL)*Exp[-I*kL*xstar]+(kL-omega)/(2*kL)*Exp[I*kL*xstar]);
fHRt4=-(I*omega)/(Sqrt[4*Pi*omega])*2*omega/(omega+kR)* Exp[-I*omega*t]*Exp[I*kR*xstar];
fHRt3=-(I*omega)/(Sqrt[4*Pi*omega])*Exp[-I*omega*t]*(Exp[I*omega*xstar]+(omega-kR)/(omega+kR)*Exp[-I*omega*xstar]);
fHRt2=-(I*omega)/(Sqrt[4*Pi*omega])*((omega-kR)/(omega+kR))*Exp[-I*omega*t]*Exp[-I*omega*xstar];
fHRt1 =-(I*omega)/(Sqrt[4*Pi*omega])*((omega-kR)/(omega+kR))*Exp[-I*omega*t]*((kL+omega)/(2*kL)*Exp[-I*kL*xstar]+(kL-omega)/(2*kL)*Exp[I*kL*xstar]);
fHRx4=1/(Sqrt[4*Pi*omega])*2*omega/(omega+kR)* Exp[-I*omega*t]*(I*kR)*Exp[I*kR*xstar];
fHRx3=1/(Sqrt[4*Pi*omega])*Exp[-I*omega*t]*((I*omega)*Exp[I*omega*xstar]+(omega-kR)/(omega+kR)*(-I*omega)*Exp[-I*omega*xstar]);
fHRx2=1/(Sqrt[4*Pi*omega])*((omega-kR)/(omega+kR))*Exp[-I*omega*t]*(-I*omega)*Exp[-I*omega*xstar];
fHRx1 =1/(Sqrt[4*Pi*omega])*((omega-kR)/(omega+kR))*Exp[-I*omega*t]*((kL+omega)/(2*kL)*(-I*kL)*Exp[-I*kL*xstar]+(kL-omega)/(2*kL)*(I*kL)*Exp[I*kL*xstar]);
fHL4=0;           
fHL3=0;
fHL2=1/(Sqrt[4*Pi*omega])*Exp[I*omega*t]*Exp[-I*omega*xstar];             fHL1=1/(Sqrt[4*Pi*omega])*Exp[I*omega*t]*( (kL+omega)/(2*kL)*Exp[-I*kL*xstar]+ (kL-omega)/(2*kL)*Exp[I*kL*xstar]);

fHLt4=0;
fHLt3=0;
fHLt2=(I*omega)/(Sqrt[4*Pi*omega])*Exp[I*omega*t]*Exp[-I*omega*xstar];             fHLt1=(I*omega)/(Sqrt[4*Pi*omega])*Exp[I*omega*t]*( (kL+omega)/(2*kL)*Exp[-I*kL*xstar]+ (kL-omega)/(2*kL)*Exp[I*kL*xstar]);

fHLx4=0;            
fHLx3=0;
fHLx2=(-I*omega)/(Sqrt[4*Pi*omega])*Exp[I*omega*t]*Exp[-I*omega*xstar];             fHLx1=1/(Sqrt[4*Pi*omega])*Exp[I*omega*t]*( (kL+omega)/(2*kL)*(-I*kL)*Exp[-I*kL*xstar]+ (kL-omega)/(2*kL)*(I*kL)*Exp[I*kL*xstar]);

I41Lower1=Coth[Pi*omega/kappa]*((fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]*(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, (Conjugate[(fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})])])*(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}));

I41Lower2=FullSimplify[ComplexExpand[I41Lower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ]

I41Lower4=I41Lower2;

I41Upper1=Coth[Pi*omega/kappa]*((fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHR1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHL1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}));

I41Upper2=FullSimplify[ComplexExpand[I41Upper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ]

I41Upper4=I41Upper2;

I41LRLower1=Csch[Pi*omega/kappa]*((fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRLower2=FullSimplify[ComplexExpand[I41LRLower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ]
I41LRLower4=I41LRLower2;

I41LRUpper1=Csch[Pi*omega/kappa]*((fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHL1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]])+(fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHR1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRUpper2=FullSimplify[ComplexExpand[I41LRUpper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41LRUpper4=I41LRUpper2;

I41ttLower1=Coth[Pi*omega/kappa]*(((fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+((fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}));
I41ttLower2=FullSimplify[ComplexExpand[I41ttLower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41ttLower4=I41ttLower2

I41ttUpper1=Csch[Pi*omega/kappa]*(((fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHRt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+((fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHLt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}));
I41ttUpper2=FullSimplify[ComplexExpand[I41ttUpper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41ttUpper4=I41ttUpper2;

I41LRttLower1=Csch[Pi*omega/kappa]*((fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRttLower2=FullSimplify[ComplexExpand[I41LRttLower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41LRttLower4=I41LRttLower2

I41LRttUpper1=Csch[Pi*omega/kappa]*((fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHLt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHRt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRttUpper2=FullSimplify[ComplexExpand[I41LRttUpper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41LRttUpper4=I41LRttUpper2;

I41xxLower1=Coth[Pi*omega/kappa]*(((fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+((fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}));
I41xxLower2=FullSimplify[ComplexExpand[I41xxLower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41xxLower4=I41xxLower2

I41xxUpper1=Coth[Pi*omega/kappa]*(((fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHRx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+((fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHLx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}));
I41xxUpper2=FullSimplify[ComplexExpand[I41xxUpper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41xxUpper4=I41xxUpper2

I41LRxxLower1=Csch[Pi*omega/kappa]*((fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRxxLower2=FullSimplify[ComplexExpand[I41LRxxLower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41LRxxLower4=I41LRxxLower2

I41LRxxUpper1=Csch[Pi*omega/kappa]*((fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHLx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHRx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRxxUpper2=FullSimplify[ComplexExpand[I41LRxxUpper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41LRxxUpper4=I41LRxxUpper2

I41xtLower1=Coth[Pi*omega/kappa]*(((fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+((fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}));
I41xtLower2=FullSimplify[ComplexExpand[I41xtLower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41xtLower4=I41xtLower2

I41xtUpper1=Coth[Pi*omega/kappa]*(((fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHRt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+((fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHLt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}));
I41xtUpper2=FullSimplify[ComplexExpand[I41xtUpper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41xtUpper4=I41xtUpper2

I41LRxtLower1=Csch[Pi*omega/kappa]*((fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRxtLower2=FullSimplify[ComplexExpand[I41LRxtLower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ]

I41LRxtLower4=I41LRxtLower2;

I41LRxtUpper1=Csch[Pi*omega/kappa]*((fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHLt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHRt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRxtUpper2=FullSimplify[ComplexExpand[I41LRxtUpper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41LRxtUpper4=I41LRxtUpper2;

I41txLower1=Coth[Pi*omega/kappa]*(((fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+((fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}));
I41txLower2=FullSimplify[ComplexExpand[I41txLower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41txLower4=I41txLower2

I41txUpper1=Coth[Pi*omega/kappa]*(((fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHRx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+((fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHLx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}));
I41txUpper2=FullSimplify[ComplexExpand[I41txUpper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41txUpper4=I41txUpper2

I41LRtxLower1=Csch[Pi*omega/kappa]*((fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRtxLower2=FullSimplify[ComplexExpand[I41LRtxLower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41LRtxLower4=I41LRtxLower2

I41LRtxUpper1=Csch[Pi*omega/kappa]*((fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHLx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHRx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRtxUpper2=FullSimplify[ComplexExpand[I41LRtxUpper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41LRtxUpper4=I41LRtxUpper2

I41t1Lower1=Coth[Pi*omega/kappa]*(((fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+((fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}));

I41t1Lower2=ComplexExpand[I41t1Lower1] ;

I41t1Lower4=Simplify[I41t1Lower2,{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0, mR^2-omega^2>0}, TimeConstraint->50 ]

I41t1Upper1=Coth[Pi*omega/kappa]*(((fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHR1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+((fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHL1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}));
I41t1Upper2=FullSimplify[ComplexExpand[I41t1Upper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41t1Upper4=I41t1Upper2

I41LRt1Lower1=Csch[Pi*omega/kappa]*((fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRt1Lower2=FullSimplify[ComplexExpand[I41LRt1Lower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41LRt1Lower4=I41LRt1Lower2

I41LRt1Upper1=Csch[Pi*omega/kappa]*((fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHL1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHR1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLt4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRt1Upper2=FullSimplify[ComplexExpand[I41LRt1Upper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41LRt1Upper4=I41LRt1Upper2;

I41t2Lower1=Coth[Pi*omega/kappa]*(((fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+((fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}));
I41t2Lower2=FullSimplify[ComplexExpand[I41t2Lower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41t2Lower4=I41t2Lower2

I41t2Upper1=Coth[Pi*omega/kappa]*(((fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHRt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+((fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHLt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}));
I41t2Upper2=FullSimplify[ComplexExpand[I41t2Upper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41t2Upper4=I41t2Upper2

I41LRt2Lower1=Csch[Pi*omega/kappa]*((fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRt2Lower2=FullSimplify[ComplexExpand[I41LRt2Lower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41LRt2Lower4=I41LRt2Lower2

I41LRt2Upper1=Csch[Pi*omega/kappa]*((fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHLt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]])+(fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHRt1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRt1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRt2Upper2=FullSimplify[ComplexExpand[I41LRt2Upper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41LRt2Upper4=I41LRt2Upper2

I41x1Lower1=Coth[Pi*omega/kappa]*(((fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+((fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}));
I41x1Lower2=FullSimplify[ComplexExpand[I41x1Lower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41x1Lower4=I41x1Lower2

I41x1Upper1=Coth[Pi*omega/kappa]*(((fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHR1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+((fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHL1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}));
I41x1Upper2=FullSimplify[ComplexExpand[I41x1Upper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41x1Upper4=I41x1Upper2

I41LRx1Lower1=Csch[Pi*omega/kappa]*((fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRx1Lower2=FullSimplify[ComplexExpand[I41LRx1Lower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41LRx1Lower4=I41LRx1Lower2

I41LRx1Upper1=Csch[Pi*omega/kappa]*((fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHL1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHRx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHL1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]])+(fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHR1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHLx4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHR1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRx1Upper2=FullSimplify[ComplexExpand[I41LRx1Upper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41LRx1Upper4=I41LRx1Upper2

I41x2Lower1=Coth[Pi*omega/kappa]*(((fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+((fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]]*fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}));
I41x2Lower2=FullSimplify[ComplexExpand[I41x2Lower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41x2Lower4=I41x2Lower2

I41x2Upper1=Coth[Pi*omega/kappa]*(((fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHRx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+((fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]+Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]]*fHLx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}));
I41x2Upper2=FullSimplify[ComplexExpand[I41x2Upper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41x2Upper4=I41x2Upper2;

I41LRx2Lower1=Csch[Pi*omega/kappa]*((fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]])+(fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})*(fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR>omega,mL>0, omega∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2, kR->I*Sqrt[mR^2-omega^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRx2Lower2=FullSimplify[ComplexExpand[I41LRx2Lower1],{mR>omega,mL>0, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals,Sqrt[mR^2-omega^2]>0,Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];

I41LRx2Lower4=I41LRx2Lower2

I41LRx2Upper1=Csch[Pi*omega/kappa]*((fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHLx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHR4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHLx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]])+(fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})*(fHRx1/.{xstar->xstar2, t->t2, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]})+(Assuming[{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[fHL4/.{xstar->xstar1, t->t1, kR->Sqrt[omega^2-mR^2],  kL->Sqrt[mL^2+omega^2]}]])*(Assuming[{mR<omega, omega∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0}, Conjugate[(fHRx1/.{xstar->xstar2, t->t2,kR->Sqrt[omega^2-mR^2], kL->Sqrt[mL^2+omega^2]})]]));
I41LRx2Upper2=FullSimplify[ComplexExpand[I41LRx2Upper1],{mR<omega, omega∈Reals,xstar1∈Reals,t1∈Reals,xstar2∈Reals,t2∈Reals, Sqrt[omega^2-mR^2]>0, Sqrt[mL^2+omega^2]>0, omega>0},  TimeConstraint-> 60 ];
I41LRx2Upper4=I41LRx2Upper2

<<"C:\Users\dudlra13\Dropbox\BH\BEC\Massive\DensityDensity\AnalyticModeSolutions\ToyModel\AnalyticChecks\DD Function\ToMatlab.m"

(*<<"D:\\Dropbox\\BH\\BEC\\Massive\\DensityDensity\\AnalyticModeSolutions\\ToyModel\\AnalyticChecks\\DD Function\\ModeDefinitions\\ToMatlab.m"*)

IDataTable41Upper={{"function[I41Upper, I41ttUpper, I41xxUpper, I41xtUpper, I41txUpper, I41x1Upper, I41x2Upper, I41t1Upper, I41t2Upper]=IDataTable41Upper(xstar1, xstar2, t1, t2, mR, mL, kappa)"},{StringJoin["I41Upper=@(omega, t) ", ToMatlab[I41Upper4]]},{StringJoin["I41ttUpper=@(omega, t) ", ToMatlab[I41ttUpper4]]},{StringJoin["I41xxUpper=@(omega, t) ", ToMatlab[I41xxUpper4]]},{StringJoin["I41xtUpper=@(omega, t) ", ToMatlab[I41xtUpper4]]},{StringJoin["I41txUpper=@(omega, t) ", ToMatlab[I41txUpper4]]},{StringJoin["I41x1Upper=@(omega, t) ", ToMatlab[I41x1Upper4]]},{StringJoin["I41x2Upper=@(omega, t) ", ToMatlab[I41x2Upper4]]},{StringJoin["I41t1Upper=@(omega, t) ", ToMatlab[I41t1Upper4]]},{StringJoin["I41t2Upper=@(omega, t) ", ToMatlab[I41t2Upper4]]}};
IDataTable41Lower={{"function[I41Lower, I41ttLower, I41xxLower, I41xtLower, I41txLower, I41x1Lower, I41x2Lower, I41t1Lower, I41t2Lower]=IDataTable41ULower (xstar1, xstar2, t1, t2, mR, mL, kappa)"},{StringJoin["I41Lower=@(omega, t) ", ToMatlab[I41Lower4]]},{StringJoin["I41ttLower=@(omega, t) ", ToMatlab[I41ttLower4]]},{StringJoin["I41xxLower=@(omega, t) ", ToMatlab[I41xxLower4]]},{StringJoin["I41xtLower=@(omega, t) ", ToMatlab[I41xtLower4]]},{StringJoin["I41txLower=@(omega, t) ", ToMatlab[I41txLower4]]},{StringJoin["I41x1Lower=@(omega, t) ", ToMatlab[I41x1Lower4]]},{StringJoin["I41x2Lower=@(omega, t) ", ToMatlab[I41x2Lower4]]},{StringJoin["I41t1Lower=@(omega, t) ", ToMatlab[I41t1Lower4]]},{StringJoin["I41t2Lower=@(omega, t) ", ToMatlab[I41t2Lower4]]}};
IDataTable41LRUpper={{"function[I41LRUpper, I41LRttUpper, I41LRxxUpper, I41LRxtUpper, I41LRtxUpper, I41LRx1Upper, I41LRx2Upper, I41LRt1Upper, I41LRt2Upper]=IDataTable41LRUpper(xstar1, xstar2, t1, t2, mR, mL, kappa)"},{StringJoin["I41LRUpper=@(omega, t) ", ToMatlab[I41LRUpper4]]},{StringJoin["I41LRttUpper=@(omega, t) ", ToMatlab[I41LRttUpper4]]},{StringJoin["I41LRxxUpper=@(omega, t) ", ToMatlab[I41LRxxUpper4]]},{StringJoin["I41LRxtUpper=@(omega, t) ", ToMatlab[I41LRxtUpper4]]},{StringJoin["I41LRtxUpper=@(omega, t) ", ToMatlab[I41LRtxUpper4]]},{StringJoin["I41LRx1Upper=@(omega, t) ", ToMatlab[I41LRx1Upper4]]},{StringJoin["I41LRx2Upper=@(omega, t) ", ToMatlab[I41LRx2Upper4]]},{StringJoin["I41LRt1Upper=@(omega, t) ", ToMatlab[I41LRt1Upper4]]},{StringJoin["I41LRt2Upper=@(omega, t) ", ToMatlab[I41LRt2Upper4]]}};
IDataTable41LRLower={{"function[I41LRLower, I41LRttLower, I41LRxxLower, I41LRxtLower, I41LRtxLower, I41LRx1Lower, I41LRx2Lower, I41LRt1Lower, I41LRt2Lower]=IDataTable41LRULower (xstar1, xstar2, t1, t2, mR, mL, kappa)"},{StringJoin["I41LRLower=@(omega, t) ", ToMatlab[I41LRLower4]]},{StringJoin["I41LRttLower=@(omega, t) ", ToMatlab[I41LRttLower4]]},{StringJoin["I41LRxxLower=@(omega, t) ", ToMatlab[I41LRxxLower4]]},{StringJoin["I41LRxtLower=@(omega, t) ", ToMatlab[I41LRxtLower4]]},{StringJoin["I41LRtxLower=@(omega, t) ", ToMatlab[I41LRtxLower4]]},{StringJoin["I41LRx1Lower=@(omega, t) ", ToMatlab[I41LRx1Lower4]]},{StringJoin["I41LRx2Lower=@(omega, t) ", ToMatlab[I41LRx2Lower4]]},{StringJoin["I41LRt1Lower=@(omega, t) ", ToMatlab[I41LRt1Lower4]]},{StringJoin["I41LRt2Lower=@(omega, t) ", ToMatlab[I41LRt2Lower4]]}};

OutputUpper= "C:\\Users\\dudlra13\\Dropbox\\BH\\BEC\\Massive\\DensityDensity\\AnalyticModeSolutions\\ToyModel\\AnalyticChecks\\DD Function\\ModeDefinitions\\IDataTable41Upper.m";
OutputLower= "C:\\Users\\dudlra13\\Dropbox\\BH\\BEC\\Massive\\DensityDensity\\AnalyticModeSolutions\\ToyModel\\AnalyticChecks\\DD Function\\ModeDefinitions\\IDataTable41Lower.m";

OutputUpperLR= "C:\\Users\\dudlra13\\Dropbox\\BH\\BEC\\Massive\\DensityDensity\\AnalyticModeSolutions\\ToyModel\\AnalyticChecks\\DD Function\\ModeDefinitions\\IDataTable41LRUpper.m";
OutputLowerLR= "C:\\Users\\dudlra13\\Dropbox\\BH\\BEC\\Massive\\DensityDensity\\AnalyticModeSolutions\\ToyModel\\AnalyticChecks\\DD Function\\ModeDefinitions\\IDataTable41LRLower.m";

(*OutputUpper= "D:\\Dropbox\\BH\\BEC\\Massive\\DensityDensity\\AnalyticModeSolutions\\ToyModel\\AnalyticChecks\\DD Function\\ModeDefinitions\\IDataTable41Upper.txt"
OutputLower= "D:\\Dropbox\\BH\\BEC\\Massive\\DensityDensity\\AnalyticModeSolutions\\ToyModel\\AnalyticChecks\\DD Function\\ModeDefinitions\\IDataTable41Lower.txt"*)

Export[OutputUpper,Flatten[ IDataTable41Upper ], "Table", "FieldSeperators"->" "]

Export[OutputLower,Flatten[ IDataTable41Lower], "Table", "FieldSeperators"->" "]

Export[OutputUpperLR,Flatten[ IDataTable41LRUpper ], "Table", "FieldSeperators"->" "]

Export[OutputLowerLR,Flatten[ IDataTable41LRLower], "Table", "FieldSeperators"->" "]