TZ =00 7Z

11 1 — gin-i IX ,^2/t-l

^ e^O.'^.^-^ TT ' ~ '^^"'~' ^"'^'^'^ ^ ^""'^

■V^ 4ûr27J — 1

^ ' ^(l— 9-271)2 ^(l— gf27i-l)2 ^(n-5r27i-l)2 ^(^i

FORMULES

co,

«Oj

^«ig'îg 2

9 T r»Wa

ixUJj i^tUj JZtU^

v/e2— 63=— -^4gr2^|g,2,

/ei

J/e2 — 63 = 1 4/ -^ 2 ^0 gr| g,T

(4) \ v/(/= v^ej— es v^ei— esV^ei — ^2= ^'^ y ^ ^^S'o S'S

g'(X(Oi, Xws) = ^ g'(wi, 103).

n=:oo / 1 \^

(i) S-i(p) = > (— i)«2(7 sin(2/7 -H j)Trp = 25-* sinTiP — 25-* sinSrp -

(li) Sr2(p)= >2^ ' cos{2n -i-i)Tzv — Q.g'' cos-KV -h •2.g'' cosi'Ki' -^-. . .,

(3) S^sCp) — I -r- \ 2<7"" cos lUTCv = \ -\- iq cosaTiP' -\- iq'* cos4Trt' -+-.-.,

(4) 3'4(>') = ' + ^( — i)'^2g"^ cos2m:v = 1 — 2 5r cos2th^ + 2q'' cos4i^^' —

(5) ?Si{v)— -^q^^q^ è\nvK\ I (i — iq^"^ co%ivk -\- q^"-),

(6) 3r2(p) = i^TQ^r* cosPTc I î {i-h 'iq^"' C0S2VK -T- q'*"),

(7) Sr3(i^)='7o JJ(i+2g'2«-icos2PTr + 5r*«-2),

n = oo

(8) •^4(f')= ^ToTTCi — 2g'27t-icos2P7r + g'*«-2),

(9) .^^^uo-rUc-o^/^'K-J,

irjv» __ / 1 f\'

(ro) e ^ 2r2(p)= ^^e V 2 W,

FORMULES. 353

XXXII (fin).

(. bis) p,(z)=. '^^(-ly'gi"^!) ,2„+.,

i'ibis) p2(-)= ^q("^^) z'-n+r,

(ibis) p3(2j= 2^"'^""'

{\bis) ?i(-)= 21(— 0"^"'-^",

(-bis) p3(-)-g'0 JJ(t + ^2«-l--2) JJ(,t^2«-l,2)^

« = n rt = 30

(8 6iS) p4(5) = '7o£J (l — g'2«-l^-2) TT (i qin-l -2)^

pi(^) = ?i(e'"^0 =2ri{('),

(4) ^o^ltfsM^e^vi.w.-'Sr.Cp),

(5) tf« = 2a)i|^e^^i'-.''%

(7) ^" ~~^ ^ 20)1 2ri(p)'

7)1 M i Srâ+i(p)

(9) i/i^^/y^a ^.-e^^.-^.-'SriCO,

(10) */^^i;3^c'ia = ie2'î.«,..^2r2(p),

(11) */i^yeI^r73a'2« = e'-^'«""2r3(0,

(12) i/^ yj;=r^,^,u = e^^-^^^>-'%{v).

FORMULES

Zéros {modulis i, x).

Sr*

S,(pH i) = 2r,((;), 2r2(P-M)=-&2(p),

^l(v -^ ni-h n-z) — {— i)'n+n q-n'- e-irn'ni^^ç^

2r2((^ H- /n -t- nz) = (— i)'« ^r-^'e-s^^Tti^j^, 2r3(p-h m-H «x) = g'-n'e-2«'''î'3r3t^,

p'i(-r)= -g'-i2r'i(o), j 2r'3(T) = -2tTr^-i2r3(o),

y.^ {m -+- ni) =(— ly+^ariraq-"'- ^2(0), -^ j 2r'3(m-+-/iT) = — 2 7iTTig-"'2r3(o),

2r'7il^)=-.-7r^"-b3(o),

FORMULES

— iq^ -\- iq'* -\-iq '' -h..., = I — iq -+- •iq'* — •2 5'9+...,

?S\{o) = 'nzqlq'% ?!i(o) =iqoq\ q" ,

y 2 Wi y 2 trii

y "3. Ml y -Util

i \/e-î — es \Jex — e^ y/ei — eo

8wf

y/e,— 63 = ^2r^(o), y/ei— 63= 3^2 (o), /g, — <?, = -J 2r| (o^,

2Wi 2Wi 2C0|

(6) 3Ko) = ^Ko)-+-3r|(oX

e,= ir— ) [+S|(o)-^t(o)],

e3=3(^— J l-^Ko)-^l(o)], «3-6.^=^— 2r*,^^(o), pour p>Y,

^,= -^ A [2r|(o)4-3r|(o)-2r|(o)2rKo)]