Darrozes 
Z=2,(s)+H*(s,¥) (7) 
with the condition : H-( s, Y )»o when Y_,0 for any s. The behaviour of 
functions H*when Y goes to zero is obtained using the reverse functions 
Gt=u7"* The identity : Y= Gt( s, H(s, Y) ) is expanded into Taylor 
series for small values of H: 
ee ed a8 +2 
YVisOaeHs oct way AHeTew else 
The following results are found. 
a) Round leading edge aft = 0, a ~ <o 
Z 2 Yond aay 
ees) = = + O(Y% 8 
nage) fi E - gihap + 0 298) (8) 
b) Sharp trailing edge a,~ # o 
wis Vie. sap tye lust wllam) ona cas . 
orate) + se Zid apap lt a) Proce iy 
c) The transitions point Iand J. Assuming that s (I) = 0, we must 
have a,(s)=0 sz20;a,(s)#0 s>0, and conversely for the 
other point J - 
When s-.0+t we admit the following expansion 
ay is: pay vee OCs) a>l1 
In that case the behaviour of the body equation in the vicinity of point I, 
depends upon the way in which s and Y goes to zero. In other words, 
the expansion (9) is not uniformly valid when s goes to zero. Itis 
possible to write a uniformly valid approximation of the function 
H ( a = = - z,(s), for any limiting process (s-.o and 
Y¥=5 0. )4" rhe corresponding description is given when Y and s go to 
zero simultaneously: Y=+4(s )¥, withu(s)+.0 when s-—>0, 
and Y has a fixed value. The function &( s) is determined by using 
the less degeneracy principle. Writting 
vas = = == om 
H (Us, Y )= HCsey ) = Bets: *5 “we khow"that fit SY) or eee 
s_»o for a fixed value of v » and 
(ies Ce ween {Bo ( 
Y = a, H +—*H* + 3H?+., 
we obtain : one he ak 5 
uH(s) Y=3, str (s){ H+...) ESPae (iety| Ba, WA +2 
In order to take into account the greatest number of terms in the 
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