cumulants of w

Consider the normal density with mean v0+t and variance 1 for w. The log of the density is foo60.

Then,we define foo61 by   This foo61 is a polynomial function of w.

Get the coefficients of 's for foo61, and store them in foo62 below.

Apply "logeexppoly" to foo62.  We get foo64=

Get the coefficients of , and multiply so that we get .

should be zero.

{v0 + o*(cr[0] + cr[2] + v0^2*cr[2] + td[al1, au1]) + 
  o^2*(v0^3*(2*cr[2]^2 + cr[3]) + v0*(cr[1] + 2*cr[0]*cr[2] + 
      6*cr[2]^2 + 3*cr[3] - 2*td[al1, au2]*td[al2, au1] + 
      td[al1, au1]*(2*cr[2] - tp3[9, 9, 9]/2) - 
      cr[2]*tp3[9, 9, 9] - (5*tp3[9, 9, al1]*tp3[9, 9, au1])/8 + 
      td[au1, au2]*tp3[9, al1, al2] - 
      (tp3[9, al1, au2]*tp3[9, al2, au1])/2 + tp4[9, 9, al1, au1]/
       4)), 1 + o*v0*(4*cr[2] - tp3[9, 9, 9]) + 
  o^2*(2*cr[1] + 4*cr[0]*cr[2] + 14*cr[2]^2 + 6*cr[3] - 
    2*td[al1, au2]*td[al2, au1] + td[al1, au1]*
     (4*cr[2] - tp3[9, 9, 9]) - 2*cr[2]*tp3[9, 9, 9] - 
    tp3[9, 9, al1]*tp3[9, 9, au1] + 2*td[au1, au2]*
     tp3[9, al1, al2] - tp3[9, al1, au2]*tp3[9, al2, au1] + 
    v0^2*(16*cr[2]^2 + 6*cr[3] - 4*cr[2]*tp3[9, 9, 9] + 
      tp3[9, 9, 9]^2 + (tp3[9, 9, al1]*tp3[9, 9, au1])/4 - 
      tp4[9, 9, 9, 9]/2) + tp4[9, 9, al1, au1]/2), 
 o*(6*cr[2] - tp3[9, 9, 9]) + o^2*v0*(60*cr[2]^2 + 18*cr[3] - 
    18*cr[2]*tp3[9, 9, 9] + 3*tp3[9, 9, 9]^2 - tp4[9, 9, 9, 9]), 
 o^2*(96*cr[2]^2 + 24*cr[3] - 24*cr[2]*tp3[9, 9, 9] + 
   3*tp3[9, 9, 9]^2 - tp4[9, 9, 9, 9])}