Tinv={{D1[s]/(2 Sqrt[s] G1), lam/Sqrt[s]},{lam/Sqrt[s],D2[s]/(2 Sqrt[s] G2)}};

D1[s_]=M1^2 - s -2 I Sqrt[s/4-mpi^2] G1; D2[s_]= M2^2-s -2 I Sqrt[s/4 - mK^2] G2;
lam=0.1; M1=0.87; M2=0.92; mpi=0.138; mK=0.496; G1=0.7; G2=1.0;

DD[s_]= D1[s] D2[s] - 4lam^2 G1 G2;

T={{2 Sqrt[s]G1  D2[s]/DD[s],-4 Sqrt[s] lam G1 G2/DD[s]},{-4 Sqrt[s] lam G1 G2/DD[s],2 Sqrt[s] G2 D1[s]/DD[s]}};

t11[s_]=T[[1]][[1]];

t12[s_]=T[[1]][[2]];

t21[s_]=T[[2]][[1]];

t22[s_]=T[[2]][[2]];

inelas[s_]=Sqrt[s/4-mpi^2] Sqrt[s/4-mK^2] Abs[t12[s]/Sqrt[s]]^2;

Plot[inelas[EE^2],{EE,2 mK, 1.3}]

C1[s_]=0.0872 +0.24 s; C2[s_]=0.5563-0.0050 s;

F1[s_]=C1[s] t11[s]/Sqrt[s] +C2[s] t21[s]/Sqrt[s];

Limit[F1[s],s->0]

D[F1[s],s];

Limit[%,s-> 0]

F2[s_]=C1[s] t12[s]/Sqrt[s] +C2[s] t22[s]/Sqrt[s];

Limit[F2[s],s->0]

D[F2[s],s];

Limit[%,s->0]

Table[{0.3+0.1 i,F1[(0.3+0.1 i)^2],Abs[F1[(0.3+0.1 i)^2]]^2},{i,0,12}] // MatrixForm

Table[{1+i 0.1,Abs[F2[(1+0.1 i)^2]]^2},{i,0,5}] // MatrixForm

fpi[s_]=1/4 Abs[F1[s]]^2/(s 0.105^2) Sqrt[1-4 mpi^2/s]/Sqrt[1-4 0.105^2/s]^3;

fk[s_]=1/4 Abs[F2[s]]^2/(s 0.105^2) Sqrt[1-4 mK^2/s]/Sqrt[1-4 0.105^2/s]^3 HeavisideTheta[s-4 mK^2];

Plot[{fpi[EE^2],fk[EE^2]},{EE,0.3,2.5},PlotRange-> {0,100}]