The Gaussian Case of the Lebesgue Power 
Integral for Short Crested Wave Systems. 
Equations(9.2) through(9.13) hold 
in addition | 2 2 2 
if (Ls HK) +(8,j—-8)<8 
then Eo (sK41,9)+1) —E2(wx,9j) < €(8) 
and O< ¥(u,8)< 27 
P(O< V(HansG2p+i)< 4 277) = @ 
where OSa=) 
then equations (9.22) and (9.24) still hold. 
also if E,(n,8) has continuous first derivatives 
67Ea(u, 4) 
on 08 
=[Ao(#,8)]°aude 
alternate formulation of integral 
Tr 
2 2 
(X,Y, 4) [foe cos8+ysin8)—pt +¥(1,8)|VAa(# Olean de 
iyi 
wT 
2 
d°E.( 4,0) = dud@ 
(9.41) 
(942) 
(9.43) 
(9.44) 
(9.45) 
(9.46) 
(9.4 7) 
S-! RI 2 
MX, tf) ee 2 -cos(B20tl(xcos@,,,,+ysin8,,4,)-Hansit+¥ Hens! Gopal 
—— + . ano an 
z O50 V (Aol Hons Pope (H2n+2 —H2n(Or945- 929) 
A\po 
Abo (Monet) 
=lim Re>d-> @ 
s-1 RoI i eacaalh cos 855 atysing, o+t) Hansit +¥(Hansl,O2p4))) 
H2s—>@ Tia picks, aii ea a 
(Az(HanstO2pei)) (H2n+ez2 2a) (O55407 65) (9.48) 
Plate XLL 
-22I- 
