f- A" sn

Multiplication.

2 snz< cnM dnw

sn 2 a = ^- — T >

I — A:2 sn*M

cn^a — sn^a dn^w

dn aa =

I — A2 sn*M dn2 M — k^ sn2 w en* m I — k^ sn*a

Transformation d'ordre impair.

LXXXYI.

t\ v/e2 — E3 Sr|(oUx) i^^YJ ti {"^^ ... \

v/ei-e, ^!(o|/^^);,„TTt2 /^^

wi I ,

2r2(o 1 ni)

,(o| /it) (/-= r,, r.2, . .., /-/i-i).

M-'^-Z^-'ff^"^'^")

v/ei— Es AA tî /^ (

ncn^a;.,o ^ y// TT t

/r = r,, /■,, •••>''«- iV

(6) L = ^&l(o|nx)='^v/E.-E3-;;^:

(7) L =-.-L=: ^a)3v/Ei-E3= j^-

FORMULES. 295

dna,. 0

(/• = Ti, r2, r,i-i).

(^> ^"(m^O = m'""II

i — A2sn2a;.,o sn^M

I — - sn^u

dn(^,^)=dn«JJ-

,„ cn-ar 0 1 — A:2 -V— — ^sn2w

dn^a^, 0

k- sn'^ar 0 ^ii^"

fr= /-,, r-i, ..., r„t\.

(7) sn f j^, n = -^ J^sn(M + 2a,.,o

/ a ,\ kM v'

(8) en f — , n = -p^cn(M-^2ar,o),

(9) dn(^^, /j = M 2]dn(Jf-l-2a,.,o),

c^ / T \ ^ ±JL dnao.j-

âr, ol-

'ei— es

cnao.r

A TT ï— ,

\/E', — Ei Al dnao,rSnao,r (i//c)" H snao.r'

(fi) (7)

A = ^ SrH o Jj = w, v/e'i - - E'3

ni t 71 * ^ nM

FORMULES. 297

(2) cnl^,\\= cnwJJ

I TT sn(M -i- ao,r)

cn(M -i- ao,r)

cnao r

(3) dn ^rj, A = dnw I I — -j— —^

\M J.1 dn(ao,r)

(r = ri,r2, ...,/-„i).

(4) Sn— ,À=-r5SnM|| T- r ^ r—

dn2a(, ,. sn^M

.n(^,x)= cnaQ^-

cn2ao,r

(6) ^"'iw'^)^ ''''"11 1

dn2«„,.

A-sn^ao ^.sn^u'

sn /

-i) 2 en

n— I -i)"2 dn

(^^ Xj = ^/ 2^dn(a-h2ao.r), ('■)

= ro. n,/-., ...,r„i).

Multiplication.

2|JlK-4-2vK't

(i) (-1) ' sn(n«) =-(-!)•'■' {s/k)"' ' JJsn(«-Hajj„v),

(IJ-.v)

(2 cn(nM)r=(X j JJcn(aH-a(x,v),