(* tperiod.m  generated by shiga3_tperiod(); 
*)
imax=2;
rule={z1->1,z2->1,z3->1,z5->1};
f1=((z5)^(b))*((z4)^(-2*b-1/2))*((z3)^(b))* Sum[(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(b)+(0)*n1+(1)*n2])(1/Gamma[1+(-2*b-1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(b)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}];
f2=((z4)^(-1/2))*((z2)^(-b))*((z5)^(b))* Sum[(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(-b)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(-1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(b)+(0)*n1+(1)*n2])*(((z5)^(n2))*((z3)^(n1))*((z2)^(n1))*((z1)^(n2))*((z4)^(-2*n1-2*n2))),{n1,0,imax},{n2,0,imax}]-((z5)^(b))*((z4)^(-2*b-1/2))*((z3)^(b))* Sum[(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(b)+(0)*n1+(1)*n2])(1/Gamma[1+(-2*b-1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(b)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}];
f3=((z1)^(-b))*((z4)^(-1/2))*((z3)^(b))* Sum[(1/Gamma[1+(-b)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(b)+(0)*n1+(1)*n2])(1/Gamma[1+(-1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}]-((z5)^(b))*((z4)^(-2*b-1/2))*((z3)^(b))* Sum[(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(b)+(0)*n1+(1)*n2])(1/Gamma[1+(-2*b-1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(b)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}];
f4=((z5)^(b))*((z4)^(-2*b-1/2))*((z3)^(b))* Sum[(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(b)+(0)*n1+(1)*n2])(1/Gamma[1+(-2*b-1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(b)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}]-((z4)^(-1/2))*((z2)^(-b))*((z5)^(b))* Sum[(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(-b)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(-1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(b)+(0)*n1+(1)*n2])*(((z5)^(n2))*((z3)^(n1))*((z2)^(n1))*((z1)^(n2))*((z4)^(-2*n1-2*n2))),{n1,0,imax},{n2,0,imax}]-((z1)^(-b))*((z4)^(-1/2))*((z3)^(b))* Sum[(1/Gamma[1+(-b)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(b)+(0)*n1+(1)*n2])(1/Gamma[1+(-1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}]+((z4)^(2*b-1/2))*((z1)^(-b))*((z2)^(-b))* Sum[(1/Gamma[1+(-b)+(1)*n1+(0)*n2])(1/Gamma[1+(-b)+(0)*n1+(1)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(2*b-1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}];
df1=((z5)^(-b))*((z4)^(2*b+1/2))*((z3)^(-b))* Sum[(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(-b)+(0)*n1+(1)*n2])(1/Gamma[1+(2*b+1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(-b)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}];
df2=((z4)^(1/2))*((z2)^(b))*((z5)^(-b))* Sum[(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(b)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(-b)+(0)*n1+(1)*n2])*(((z5)^(n2))*((z3)^(n1))*((z2)^(n1))*((z1)^(n2))*((z4)^(-2*n1-2*n2))),{n1,0,imax},{n2,0,imax}]-((z5)^(-b))*((z4)^(2*b+1/2))*((z3)^(-b))* Sum[(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(-b)+(0)*n1+(1)*n2])(1/Gamma[1+(2*b+1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(-b)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}];
df3=((z1)^(b))*((z4)^(1/2))*((z3)^(-b))* Sum[(1/Gamma[1+(b)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(-b)+(0)*n1+(1)*n2])(1/Gamma[1+(1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}]-((z5)^(-b))*((z4)^(2*b+1/2))*((z3)^(-b))* Sum[(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(-b)+(0)*n1+(1)*n2])(1/Gamma[1+(2*b+1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(-b)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}];
df4=((z5)^(-b))*((z4)^(2*b+1/2))*((z3)^(-b))* Sum[(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(-b)+(0)*n1+(1)*n2])(1/Gamma[1+(2*b+1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(-b)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}]-((z4)^(1/2))*((z2)^(b))*((z5)^(-b))* Sum[(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(b)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])(1/Gamma[1+(1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(-b)+(0)*n1+(1)*n2])*(((z5)^(n2))*((z3)^(n1))*((z2)^(n1))*((z1)^(n2))*((z4)^(-2*n1-2*n2))),{n1,0,imax},{n2,0,imax}]-((z1)^(b))*((z4)^(1/2))*((z3)^(-b))* Sum[(1/Gamma[1+(b)+(1)*n1+(0)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(-b)+(0)*n1+(1)*n2])(1/Gamma[1+(1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}]+((z4)^(-2*b+1/2))*((z1)^(b))*((z2)^(b))* Sum[(1/Gamma[1+(b)+(1)*n1+(0)*n2])(1/Gamma[1+(b)+(0)*n1+(1)*n2])(1/Gamma[1+(0)+(0)*n1+(1)*n2])(1/Gamma[1+(-2*b+1/2)+(-2)*n1+(-2)*n2])(1/Gamma[1+(0)+(1)*n1+(0)*n2])*(((z5)^(n1))*((z4)^(-2*n1-2*n2))*((z3)^(n2))*((z2)^(n2))*((z1)^(n1))),{n1,0,imax},{n2,0,imax}];
h={{h345,-h345*a,-h345*a,h345*a^2},{-h345*a,(h345+h245)*a^2,h345*a^2,(-h345-h245)*a^3},{-h345*a,h345*a^2,(h345+h134)*a^2,(-h345-h134)*a^3},{h345*a^2,(-h345-h245)*a^3,(-h345-h134)*a^3,(h345+h245+h134+h124)*a^4}};
h2=h /. {h345->((Pi)^(-(3))*(2)*Sin[Pi*(-b)]*Sin[Pi*(2*b+1/2)]*Sin[Pi*(-b)]),h245->((Pi)^(-(3))*(2)*Sin[Pi*(b)]*Sin[Pi*(1/2)]*Sin[Pi*(-b)]),h134->((Pi)^(-(3))*(2)*Sin[Pi*(b)]*Sin[Pi*(-b)]*Sin[Pi*(1/2)]),h124->((Pi)^(-(3))*(2)*Sin[Pi*(b)]*Sin[Pi*(b)]*Sin[Pi*(-2*b+1/2)])};
h3=h2 /. {a->1/b};
h0=Limit[h3,b->0]
pp0={Limit[f1 /.rule,b->0],Limit[(f2/b) /. rule,b->0],Limit[(f3/b) /. rule,b->0],Limit[(f4/b^2) /. rule,b->0]};
ppDual0={Limit[df1 /. rule,b->0],Limit[(df2/b) /. rule,b->0],Limit[(df3/b) /. rule,b->0],Limit[(df4/b^2) /. rule,b->0]};
ans=ppDual0.Inverse[h0].pp0;
(* ppDual hh^(-1) pp^t = Ich^t *)
Print[N[{ans , 32} /. {z4->10}]];
Print[N[{ans , 32} /. {z4->10^2}]];
Print[N[{ans , 32} /. {z4->10^3}]];
Print["Try also Limit[D[ans,{z4,2}],z4->Infinity] or N[D[ans,{z4,2}] /. {z4->100}"];

(*
In[35]:=                                                                        InputForm[h0]
]

Out[35]//InputForm= 
{{0, 0, 0, 2/Pi}, {0, 0, 2/Pi, 0}, {0, 2/Pi, 0, 0}, {2/Pi, 0, 0, -8*Pi}}

In[36]:=                                                                        InputForm[Inverse[h0]]
]

Out[36]//InputForm= 
{{2*Pi^3, 0, 0, Pi/2}, {0, 0, Pi/2, 0}, {0, Pi/2, 0, 0}, {Pi/2, 0, 0, 0}}
*)
