XL VIII

V = oo

i^'MO-

sj(p)

sî('')

(°ro

<KaT)Y(T)=/âx(t)x(2'c).

©•fat)= — i— ^ — - — = ^— - — ->

tp(T) =

FORMULES

XLIX (fin).

qo =

Çi-e

'Kx)

v/i-çH-)=v^

aja<') =

2 5i(p) &,(>>) 5r,(t>)3r4(t>) 2r,w2rj(o)2r»(o)

^l(>')^l(>')-^î(«')aî(f) &,(o)Sî(o)

^i (0)^3,(0) ^iiv)-?!i(v) ^ ^l(t>)-2!\(v)

ai W| ^ 'itJi Al <i>i 2(oi

— = 2ÇrÎ5ro^*=3r,(o), -- =2 Qf Qo Q* = &2(o|/lT),

— =7l9'o =^3(0), -T-^^i^o =2r3(o|/iT},

— =5'3<7o =2r^(o), --=q;qo =5^(o|/IT).

0 = y = e»Tni^ V ^ • V = •

{ f — f'ii ^ii ■ • • ? ''n— 1 \ •

FORMULES

&,(n,'|„T)= ||â3(»')IX^'(''^ïï)'

(r = Ti, 7-2, . . ., r^-i).

(6) 3r,(nr|«t)=^&i^p)JJ

ir)

3r,(np!n':)= -^^i'*')]^!

^ÎC) 7T^^ <>>) 1,

^■,(o)IJ^î(^-

^a+-tC

/i 2r', (o I Al T )

if — ^ Il ''il • ' '1 ^/i— A

T. et M. - II.

^ll2l = ± = JL,iJ

3^3(0) = ^ =g\qo,

CALCUL DIFFËRE.\TIEr..

itoi * \ \nj k\ tui "

I V = co ^ j^ V=« , ^.

V = flo

îv-j\ '-"' / iv-i\

.- "ni

rrr

-ll^) =(->." q'i-'Q'.'l

nH'i)'

,/» j in —S) \l / «

li/i

iri

(/■ — /'i, Tj, . . . , r,i-i).

FORMULES

LU (fin).

(rj (r)

iv,.,

en particulier bi=: bi=^ bi = ùi = —^ » pour r=±:i,±2, ...,di — ; — ,

rn:/-,, rj

-(iTJ-!!^'^^'!!

LUI

(0 iM.)i'=^=n^œ^'(;0^'(0]

(a) v/;ïh(/it)[h(x)] » =IX3'.(^)

cp(nT)

Cp(T)

<K/it)

rTor./':\

" ,--ii.(..f--nh(")^.(^')-(T)]

,7) e . q «- h(^)[h(T)] > =lp>('i)

(2) n^-iï)

( lO)

FORXl'I.ES. 377

({JL, V) 2'*

V = O, Ti, Tf, . . ., Tn-l

378 CALCUL DIPFËBENTIBL.

n» ^^^ ni ta, izitt

4>(a) = V An^rA eî/i/w=V Anc'Âw, "'"^ co, "^

^n+h — Art,

4>(w -h aoji) = 4>(m), (2) ! Att/

4>(a) = Ao*o(w)-h A,4>,(w)-h...-f- A/,,4>A,(tt),

(/i4 4- ri'

(3) l *r(w) = 2 ^ * e«''ï<«>^-»-'-J = qf» €^^*''^^^i(hv -¥- ri: \ Ax),

(4) *o(«) = a,(apl2T), *,(a) = a,(at.|aT).

SS + l(0)a.('' + c)a,(«'-C)= Sî^,(c)&J(0-Sî(c)&J^,(i.),

aj(o)&,(t'+c)S,(f-c) =-Sj(c)Sî(p) H-2r|(c)2irî(p), 2r|(o)3,(P+c)&3(i^-c) = 2r}(c)^?(i') +&5(c)S!(''). a»(o)St(P + c)S»(.'-c) = &|(c)&î(i') -+-&J(c)&i(v),

= -S.(c)a,(c)S,(p)&,(p)H-2ir,(c)SUc)S,(i')S;(..),

= -â,(c)3r3(c)S.(,.)2r,(i-) + 3!(c)&»(c)a,(t-)&»(i'), â,(o)&,(o)a,(i' + c)St(('-c)

= -&,(c)&v(c)a,(i')&4(0 + &.(c)&3(c)S.(«')Sa(«').

FORMULES. ^79

Tp = &p(a 4- b) &p(a - 6) ^p( c -f- d) ^^{c — é/),

(1) I Tp = &p(rt-hc)&p('a-c)&p(e/4-6)&p(rf-6\ rp = &p(a -4- d) 3rp(a - c^) ?S^{b -+- c) 2rp(6 - c),

(2) T,-f-T;4-Tî = o,

T, -+- Ta = t; -h Ti = t; -4- t; , T3h-T4 = t'3-+-t; = tj-4-t;.

(i) ( x2r3[a7~?a:4-ra?T|a?(a-f.p)T]

= V 5ra'''e«'"/îtJ^&3[a:-4-7-hrat|(a-t-P)T]

X 2r3[ ?2r - a^ -f- ra?x I a? (a -4- P)t],