‹ Éléments de la théorie des fonctions elliptiques (volume 3)Chapitre 86 sur 90 · TC Z · texte numérisé non relu

TC Z

\ 37tZ,, „ /\

2\ — -(aô + crf) 7(x)

X(T) = - r pe

2 \ —-(ab-cd)

Vc) P" ^^")'

cp('c)'

■ (rtft + ac+bd — ab*c) — ^ (crf4- rtC + bd— bc*d)

— -^[8(6 — sgn6) + flc(6» — l)-ô(rt + rf))4

* * '^[„c(6'-l)-6(a + rf)] / ^ 7— Tu/ \

; 12 ^ i^oj + Ot) h(T),

Q = gr2 = e2TTO-^ V = oo V = »

= IX(i + g'^'2^-i')> Q3 = II(« - 5'^'^^-"),

(io = qoqu 03=5^2^3 = 2Q|Q,| = g'o'(5'2 + g'3)»

8Q^Q|Qt=g'g(g'|-g'^),

3ri(0-3rf(p) ^ Srl(t>)-&|(0^

2 2r2 ( o j 2 T ) Sr3(03r4(t^)

2&; (o 1 2t) Sr^Co I 2t) = 3r; (o) ^2

2Sr2(0|2x)2r3(0[2T) = Sl(0),

22ri(o|2T) = 2rKo)-2r|(o), 23r2(o|2T) = S|(o) + 2rKo),

FORMULES

1 TTtt

Qo = JJCi - 'Z^)- Q'i = JI(i + 9'^)>

V = oo

T\ 3f(p)+SKt') S|(c.)-&|(t;)

^^o|-y = 2r|(o)+2ri(o), 2^!(o|^) = 3i(o)-3r?,(o).

6/- 12A-. ll('^)

(lo)

FORMULES. 271

XLIX (fin).

(T-l)ltJ

zni h( - )

'^ ^ 27HO) 2^3(0) &4(oj '

2^2(0) ;J|(o) ~'3(,if^; — oTi — Tcn — ^ '

I TT , I 3r'. (o) I nTT , f n^'. (o\ Hz) — = ~9l9 = — ' T- = — Qo Q' = ■ ->

2 Q? Qo Q* = '^2(0 \ nz),

— =glgo =^4(0), «4

q| Qo = 3^3(0] n-û),

. — q1 Qo = ^i>{o \nx).

Ai

Q = gr« — e«T7t«^

Q2 = JJ(I + ^«'2V-1)), Q3 = JJ(I - g-^f^V-I))^

qo- q

qo

qi

(rj

n / qa

"1 îS-'? ' ?f

nâ.(^) =(-.)- îT'/"'!!

" ql

FOnMULES.

^r,(„.|;^, ) = (,)<'■) |^2r,(.)JJ:^,|^. ^^

(/• = ri, /-j, ..., r„,).

(5) ?Ji{nv\nz)

Al

(Il

(6) ^î(«^^|/iT)=g2r,(t')JI

(7) 2r3(n.|/zx)-g&3(^)JJ

(8) 2r,(nPln-) = |î^i(»JI

Aa+-i

^oL+i(o\ n-)

fr = ri,r„ ...,r„A.

SfK'^) :

T. et M. — II.

«1 Wi

LU

= T7- =2Qi2q^q'4^

Qo=fJ\' — '7'V, Q, = ■ ■ M

ïî

l)(n — 2i yi ;-2

ii- — \ yi r'-

= (-.)■" ^fT-0?7'^'^ ^"%

FORMULES

LU (fin).

, 2f7ti2j -

ir)

S'il

en particulier bi ^ b<i= 03 = O:^ = --- , pour r = rn I , ± 2, . . . , ±

m^Kv)=^n^^^.(v)=|^=^-^^,

2rf(p)

^i(^) 77^ ^KO

LUI

ir)

(2) v/nh(nT)[h(x)]"^ = Jj2?i(^).

tfCnr) (r)

''-' UH'.

(7) ^' ' 9 -^^ Mn;^'^^"^]"^^n^'(ir

cp(T)

rx

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