Faltitnsen 
vZ 2 1 
@ (x,y,z) = 2 | dk ie o*(k) F *(k) + vye a(x) 
27 V2, -00 
oo 
vZ i2vx 
e 
Lai eee 
20 4 2v a) 
Using the convolution theorem we get 
-inr/4 [* dia(&) vz 
@ (x,y,z) = - vee ae / | ———— + vy e a(x) 
7/2 V2 wrx 
LZ 
yee etx bh dent) ies 
x 
By using an asymptotic expansion of the last integral (see Erdélyi 
(1956)), (B-7) can be written as Eq. (18). 
Que (a 2 Zu). GG (B -6) 
APPENDIX.G 
Simplification of the far-field expansion in the forward-speed problem 
We will show how (59) can be rewritten into (60) and (61). 
We first introduce 
in (59). If we drop the primes we can write (59) as 
bpleyezt) = (xy,2) eto '™) (C-1) 
1818 
