density function f(u,v|v0)

is given as follows.

First, we set η=(0,...,0,v0). In other words, , and . Here we use symbol v0 for λ.

Then, change of variables y=η(u,v).

Now we get logdensityuv=foo38=f(u,v|v0).

-v^2/2 + v*v0 - v0^2/2 - (dim*Log[2*Pi])/2 - (ru[al1]*ru[au1])/2 + 
 o*(-(v0*ru[al1]*ru[al2]*td[au1, au2]) - (v^3*tp3[9, 9, 9])/6 - 
   (v0^3*tp3[9, 9, 9])/3 + v*(2*td[al1, au1] + tp3[9, 9, 9]/2 + 
     (v0^2*tp3[9, 9, 9])/2 - (v0*ru[al1]*tp3[9, 9, au1])/2 - 
     tp3[9, al1, au1]/2 + ru[al1]*ru[al2]*(-td[au1, au2] + 
       tp3[9, au1, au2]/2)) + ru[al1]*((v0^2*tp3[9, 9, au1])/2 + 
     tp3[al2, au1, au2]/2) - (ru[al1]*ru[al2]*ru[al3]*
     tp3[au1, au2, au3])/6) + 
 o^2*(-(v0*ru[al1]*ru[al2]*ru[al3]*te[au1, au2, au3]) + 
   tp3[9, 9, 9]^2/6 + (tp3[9, 9, al1]*tp3[9, 9, au1])/2 + 
   (tp3[9, al1, au2]*tp3[9, al2, au1])/2 + 
   (tp3[al1, al2, al3]*tp3[au1, au2, au3])/6 - tp4[9, 9, 9, 9]/8 - 
   (v^4*tp4[9, 9, 9, 9])/24 - (v0^4*tp4[9, 9, 9, 9])/8 + 
   v^3*ru[al1]*(-(td[au1, au2]*tp3[9, 9, al2]) + 
     (tp3[9, 9, 9]*tp3[9, 9, au1])/4 + 
     (tp3[9, 9, au2]*tp3[9, al2, au1])/2 - tp4[9, 9, 9, au1]/6) + 
   (v0^3*ru[al1]*tp4[9, 9, 9, au1])/6 + 
   v^2*(-2*td[al1, au2]*td[al2, au1] - tp3[9, 9, 9]^2/4 - 
     (tp3[9, 9, al1]*tp3[9, 9, au1])/2 + 2*td[al1, au2]*
      tp3[9, al2, au1] - (3*tp3[9, al1, au2]*tp3[9, al2, au1])/4 + 
     tp4[9, 9, 9, 9]/4 + tp4[9, 9, al1, au1]/4) - 
   tp4[9, 9, al1, au1]/4 + v*((v0^3*tp4[9, 9, 9, 9])/6 + 
     ru[al1]*ru[al2]*(-2*v0*td[al3, au2]*td[au1, au3] + 
       (v0*td[au1, au2]*tp3[9, 9, 9])/2 + 
       (3*v0*tp3[9, 9, au1]*tp3[9, 9, au2])/8 + 
       (v0*tp3[9, al3, au2]*tp3[9, au1, au3])/2 - 
       (v0*tp4[9, 9, au1, au2])/4) + 
     ru[al1]*(6*te[al2, au1, au2] + 5*td[au1, au2]*tp3[9, 9, al2] + 
       v0^2*td[au1, au2]*tp3[9, 9, al2] + td[al2, au2]*
        tp3[9, 9, au1] - (3*tp3[9, 9, 9]*tp3[9, 9, au1])/4 - 
       (v0^2*tp3[9, 9, 9]*tp3[9, 9, au1])/4 - 
       (3*tp3[9, 9, au2]*tp3[9, al2, au1])/2 - 
       (v0^2*tp3[9, 9, au2]*tp3[9, al2, au1])/2 + 
       (tp3[9, 9, au1]*tp3[9, al2, au2])/4 - 2*td[al2, au3]*
        tp3[al3, au1, au2] + (tp3[9, al2, au3]*tp3[al3, au1, au2])/
        2 - td[al2, au1]*tp3[al3, au2, au3] + 
       (tp3[9, al2, au1]*tp3[al3, au2, au3])/2 + 
       tp4[9, 9, 9, au1]/2 - tp4[9, al2, au1, au2]/2) + 
     ru[al1]*ru[al2]*ru[al3]*(-2*te[au1, au2, au3] - 
       (3*td[au2, au3]*tp3[9, 9, au1])/2 - 
       (tp3[9, 9, au3]*tp3[9, au1, au2])/4 + 
       td[al4, au3]*tp3[au1, au2, au4] - 
       (tp3[9, al4, au3]*tp3[au1, au2, au4])/2 + 
       tp4[9, au1, au2, au3]/3)) - tp4[al1, al2, au1, au2]/8 + 
   ru[al1]*ru[al2]*(2*td[al3, au2]*td[au1, au3] - 
     (v0^2*td[au1, au2]*tp3[9, 9, 9])/2 - 2*td[au2, au3]*
      tp3[9, al3, au1] - (td[au1, au2]*tp3[9, al3, au3])/2 - 
     (tp3[al3, al4, au1]*tp3[au2, au3, au4])/4 + 
     tp4[al3, au1, au2, au3]/4) + ru[al1]*ru[al2]*ru[al3]*ru[al4]*
    (-(td[au1, au2]*td[au3, au4])/2 + 
     (td[au3, au4]*tp3[9, au1, au2])/2 - tp4[au1, au2, au3, au4]/
      24))

We extract the coefficients for u, v from the density function f(u,v|v0).

-coefficients

-coefficients

-coefficients

-coefficients

-coefficients