According to the analysis of Section 3.4, we can write

(D.8) 
where

(D.9) 
Here, use has been made of Equation (D.5).
Now, to first order in
, Equation (D.6) can be inverted to give

(D.10) 
Hence, to the same order, Equation (D.9) gives

(D.11) 
Making use of Equation (3.42), we deduce that, to first order in
,
with all of the other zero.
The analysis of Section 3.4, combined with the previous two equations, also implies that

(D.14) 
where

(D.15) 
and

(D.16) 
Now, to first order in
, we can write

(D.17) 
where

(D.18) 
Substitution of Equation (D.17) into Equations (D.15) and (D.16), followed by an expansion to first order in
, yields

(D.19) 
where

(D.20) 
and
Here, we have integrated the last two terms in curly brackets by parts.