three-step multiscale bootstrap

In the below, we will calculate   =.

z2v8=z2[v8[z,v0,tau1],tau2,tau3]. This is regarded as a polynomial of z, and then intfz will be applied to z2v8.

foo11 is the O(1) term

We may make replacements b->z2v8ab[[1]], a->z2v8ab[[2]]  later for the normal integration with intfxg[a,b,n], i.e., z2v8o0=az+b.

Get the dd coefficients and store them in z2v8dd

Now the integration is = . .

Check if z3 reduces to z2 when one of the scales is zero

v/Sqrt[tau1^2 + tau2^2 + tau3^2] + 
 (o*((tau1^2 + tau2^2 + tau3^2)*(6*Daa*(tau1^2 + tau2^2 + tau3^2)^2 + 
      P999*(tau1^4 + tau2^4 + 3*tau2^2*tau3^2 + tau3^4 + 
        3*tau1^2*(tau2^2 + tau3^2))) + 
    P999*(2*tau1^4 + 2*tau2^4 + 3*tau2^2*tau3^2 + 2*tau3^4 + 
      3*tau1^2*(tau2^2 + tau3^2))*v^2))/
  (6*(tau1^2 + tau2^2 + tau3^2)^(5/2)) + 
 (o^2*(-72*Dab2*(tau1^2 + tau2^2 + tau3^2)^5*v + 
    (tau1^2 + tau2^2 + tau3^2)*(12*Daa*P999*(tau1^2 + tau2^2 + tau3^2)^2*
       (tau1^4 + tau2^4 + tau3^4) + P999^2*(-5*tau1^8 - 
        21*tau1^6*tau2^2 - 73*tau1^4*tau2^4 - 48*tau1^2*tau2^6 - 
        5*tau2^8 - 3*(7*tau1^6 + 40*tau1^4*tau2^2 + 49*tau1^2*tau2^4 + 
          7*tau2^6)*tau3^2 - (73*tau1^4 + 174*tau1^2*tau2^2 + 73*tau2^4)*
         tau3^4 - 48*(tau1^2 + tau2^2)*tau3^6 - 5*tau3^8) + 
      3*(tau1^2 + tau2^2 + tau3^2)*(-3*P99a2*(tau1^6 + 6*tau1^4*tau2^2 + 
          9*tau1^2*tau2^4 + tau2^6) - 18*P99a2*(tau1^4 + 
          3*tau1^2*tau2^2 + tau2^4)*tau3^2 - 27*P99a2*(tau1^2 + tau2^2)*
         tau3^4 - 3*P99a2*tau3^6 + 6*(4*DabP9ab + P99aa - 2*P9ab2)*
         (tau1^2 + tau2^2 + tau3^2)*(tau1^2*tau2^2 + (tau1^2 + tau2^2)*
           tau3^2) + P9999*(tau1^6 + tau2^6 + 4*tau2^4*tau3^2 + 
          10*tau2^2*tau3^4 + tau3^6 + 4*tau1^4*(tau2^2 + tau3^2) + 
          2*tau1^2*(5*tau2^4 + 9*tau2^2*tau3^2 + 5*tau3^4))))*v - 
    (P999^2*(4*tau1^8 + 4*tau2^8 + 21*tau2^6*tau3^2 + 17*tau2^4*tau3^4 + 
        12*tau2^2*tau3^6 + 4*tau3^8 + 21*tau1^6*(tau2^2 + tau3^2) + 
        tau1^4*(17*tau2^4 + 48*tau2^2*tau3^2 + 17*tau3^4) + 
        3*tau1^2*(4*tau2^6 + 13*tau2^4*tau3^2 + 10*tau2^2*tau3^4 + 
          4*tau3^6)) - 3*(tau1^2 + tau2^2 + tau3^2)*
       (-3*P99a2*(tau1^6 + 2*tau1^4*tau2^2 + tau1^2*tau2^4 + tau2^6) - 
        6*P99a2*(tau1^4 + tau1^2*tau2^2 + tau2^4)*tau3^2 - 
        3*P99a2*(tau1^2 + tau2^2)*tau3^4 - 3*P99a2*tau3^6 + 
        P9999*(3*tau1^6 + 3*tau2^6 + 8*tau2^4*tau3^2 + 6*tau2^2*tau3^4 + 
          3*tau3^6 + 8*tau1^4*(tau2^2 + tau3^2) + 
          6*tau1^2*(tau2^2 + tau3^2)^2)))*v^3))/
  (72*(tau1^2 + tau2^2 + tau3^2)^(9/2))