Dalzell’s final expressions, including the effect of higher order cumulants (until 3) 
that take account of the higher order nonlinear response until the third order, are 
p3(v) = S(v,€) € 
2/2 
+ R(v,€) (1-e7)!/2 ex(-5] Q ae . (12.166) 
p2(v) = S(v,€) € Thae 
2) 2/2 
SI2O8) (ae we ox(—5] @ os 2.167) 
Here 
Asp + es = 5e") i Aoos(1 —€2 )!/2 
e+ «4 
SQ,Ee)=14+v 
Aio2 A201 
Sogn le el —€7) 4/2 _ Jiro 
+ v°A300, (12.168) 
374 
