[ xxxiy ] INTRODUCTION, 
on a entre les quatre fonctions S- les relations 
9 x = 9-, ( — 
(4) 
) = feM* — P*) = — (’ r+ 7“P Î ) 
(x — pi)— iffS-3 (* -+- J — P'j 
^* = 9, (j = gï 3 (*-p‘}= g» (*+■[ 
— ar) = £$,{*-P*) = fiTÔ-, 
3- (o) = 9- 3 ( - ) = i — 27 4- 27* — 27“ H , 
P 1 y 
P 1 )* 
(5) 
S,(o) = S 2 
f tt\ 1 1 11 
S-, (o) = &,(-) = 27’ -h 2? 4 -+-27 4 +..., 
>.{0) = s- = I + 27+ 27*+ 27"+... 
(-6) 
Pour 
on a 
a H- m tv 4- 2 « p i, 
cj- ni 'e- inxi , 
9 a? = (—i) B X B .9 a, 
9,a? = (— i)'” + "X„..9- t a, 
9- J a?={—ï) ,B X B .9 2 a, 
9 a .r = X„.9,a. 
Soient 
(8) 
d’où 
(9) 
(10) 
§ II. 
, TT* 1 , /p 
r 4 p V P 
Æ* =« + Wir+(în + l)fl 
X„ =ç-( B+ i) , e-( 2rt+, ) xi , 
S-^7=(—1)” + 2 X B ,9 a, 
» 1 x = (- I )'” 4,î+ IX, 1 .& | a, 
9-,.r = (—i) m X rt .9 2 a, 
9,.r = X„.9, a. 
TT .T 2p Æ 
2 p TT 
PP 
vV _ 
v/p~ 2 P 
2 p _ 
7j 
r/=e~ 2 P', p'= 1 lognat. -i,- 
En faisant, pour abréger (*), 
on aura 
(") 
V = \/y.e 2 P = \Ft.e 2 P' = v/7 •'Z' 71 ' = vV?* » 
9 (¿ci) = V.9,(*', 7'), 
1 9 t (^) = Y. 9, (*', 7')j 
9 2 {*i) = Y.9 [x 1 , 7'), 
9 3 ( ^ ) = ^ • ^3 ( x 1 c l ) • 
(*) D’après la notation de Jacobi, 
7r K 
x' — 
TT U 
ÜK 7 ’ 
9(ar', q') — 0 {11, k'), etc.