where 
is the unit step function.
where
is the unit step function.
. Its Fourier transform is:
To obtain this, set 
; apply the Fourier transform to the normalwash at midchord: 
.
To use this, we must first develop an expression for cl for a case of simple harmonic gust velocity variation, then substitute the indicial gust expression n the frequency domain. As before, we seek a generalized expression where the complicated parts of the integral are computed as a general function.
Simple harmonic transverse gust:
In flow-fixed coordinates, 
, a simple harmonic spatial function. In terms of 
, non-dimensional body-fixed coordinates, 
; periodic in space and time.
Substitute in our expression for Cp in the frequency domain. Now
and 
. Substituting for Cp, we get (skipping some math here), 
, and 
.
Define
. Thus
.
Transform cl(k,t) into the frequency domain: 
and
and 
. Substituting for 
, with 
(semi-chords traveled in time t),
; 
.
is the Kussner Function. 
, or 
, both appropriate near s=0, and
, which is more appropriate away from s=0.