I-+- 2^*" cosapir -t- q

n^ae n = oe

c, u = e«i.a,... TT '-^y'"-^^-' TT ^^^'^-^^'

i^^i«-i JLX i-t-^'

'.—-n^^iSïPn

/yl/»-l

nzz.to

(.) 2^..o,=-2e.,oî + ^« 11+2(7^7^1

/!= co

(2) 2 7)1 Wi = — '2ej(i)? -4-71* > ; ^— — -

^. fi V ^y'" 1

/l=:«e /i:=ao /l = oo /i = «

FORMULES

ro,

tï'i

'iq\q'*

cfa

^1 ntw,

IX w I 1 1

V^e, — «3 = v/ci — e, =

g = (e,- e3)«(e, - e,)» (e,- e,)' = -^ (^| - 27^!) = Jg ;;;tî ^î* <?

(4) \ y&'= t^^T^^ V^ei- ea v^ei-e,= ,-^ ^-^a^J^S

Ç(Xo)i, Xo),) = ^ ^(0)1, 0)3).

a5a Calcul différentiel.

(i) 3',(i>)=>( — i)'»2^ sin(2n H-OiTi' = 2^* sin:rp — ly^sinSirp-h. . .,

(2) 3j(p)= >2^ cos(2n + i)'ïtP = 2^*cos'7ti? + 2^^'cos3icp+...,

(3) 2r3(p) = 1-4-^27"' cos2nicp = 1 + 2^ cos27rp + a^*cos4wt' -+-...,

(4) 3"4(V)= I -H^C — l)'»2^'»* COS2n7r(; = I — 2q 008 21:1^-4- 2q^ cosiizv — . . .,

(5) 3r|(p)= 2^0^* sini^TT I 1 (l — 2^*'»C0S2P1C-+- ^*'*),

(6) 3r,(p)=: 2Ço^* COSPlt I I (l -+- 2^*» C0S2P1C -4- Ç*"),

(7) 3^3(i')= qo I I (l-h25r"»-» COS2P7H-^*«-«),

«=1 /I=:ao

(8) 3r4(p)=: ^0 rT(l — 2^*'»-l COS 2 P1t-f-^ *«-*),

FORXDLES. 253

XXXII (fin).

(3éù) p.(«)= 2*"'*"'-

(ibis) p*(^)= 2^""'^"^"'''"''

/!=:« 4:= oo

(5 6m) pi(z;==2^o^^^-^4-^J^(i— 5'''''5-«)J^

n^to n= «

(7 bis) P8(-)=^o JJ(i-+-5'*""'*'3-«) JJ(i-4-^«'»-i^«),

n=:x /I = BO

(8 6w) pv(5) = î'o JJ (i — 7"»-»z-«) JJ ( I — <7««-i-5«),

Pa-t-i(^)= Pa+i(e»'^0 =&«+!(*')•

(2) 2 7o<?W^criU = c'^.««»''&,(p),

(3) ^o^îcr,a = e«ii»i«''3r,(pX

V „ "ni" I S^«-4-l(<^)

ÇaM = S; 7— r>

o), 2(0, 3ra+i(i')

(12) l/^ y^T^^cTsM = c«i»«.»'«3r4(p).

FORMULES

Zéros (modules i, t).

3fi(— «")= — ^iC»*). &a-t-i(— «') = 2fï<-i('').

Si («' + i) =&!(«'), ^«(«'+^)

3fj(i'-i-t) =

A&,(c), arj(p-+-T)

A = <jr-< c-»'»",