two-step multiscale bootstrap

In the below, we will calculate [Graphics:../Images/index_gr_1597.gif]  =[Graphics:../Images/index_gr_1598.gif].

z1v8=z1[v8[z,v0,tau1],tau2]. This is regarded as a polynomial of z, and then intfz will be applied to z1v8.

[Graphics:../Images/index_gr_1599.gif]
[Graphics:../Images/index_gr_1600.gif]

foo11 is the O(1) term

[Graphics:../Images/index_gr_1601.gif]
[Graphics:../Images/index_gr_1602.gif]
[Graphics:../Images/index_gr_1603.gif]
[Graphics:../Images/index_gr_1604.gif]

We may make replacements b->z1v8ab[[1]], a->z1v8ab[[2]]  later for the normal integration with intfxg[a,b,n], i.e., z1v8o0=az+b.

Get the dd coefficients and store them in z1v8dd

[Graphics:../Images/index_gr_1605.gif]
[Graphics:../Images/index_gr_1606.gif]
[Graphics:../Images/index_gr_1607.gif]
[Graphics:../Images/index_gr_1608.gif]

Now the integration is [Graphics:../Images/index_gr_1609.gif]= [Graphics:../Images/index_gr_1610.gif]. .

[Graphics:../Images/index_gr_1611.gif]
[Graphics:../Images/index_gr_1612.gif]

Check if z2 reduces to z1 when one of the scales is zero

[Graphics:../Images/index_gr_1613.gif]
[Graphics:../Images/index_gr_1614.gif]
[Graphics:../Images/index_gr_1615.gif]
[Graphics:../Images/index_gr_1616.gif]


Converted by Mathematica      July 21, 2003