22 SUR LE DEVELOPPEMENT EN SERIES 



* 



En remplagant les puissances des sinus par les cosinus des arcs multiples , il vient : 



(VII). 



'f " - x I 



_ 1 I [2, tt] [2iM-2, u-Hj [2U-4-2, 1] [2iH-i,'H-2] [2-f-4,2j [2(jH-u i),p+u 1] [2(/H-M 1), 



cos. i 2( 2 4 "~' 2*" + 3 a * + ' 2 *P + *- 



-f- Etc 



( !)"[>, 5] ( 1)" + '[2u+2,l][2+2, 4] (-1)" + 2 [2m-4,2][2lH-*,] ( I)' + 3 [2iH-C,S] [2u+6,6] 



( 1)"[8K,8] _ ( 1)" + ' [211+3, 1] [2u+2, 3] ( 1)* * ' [2u+4, 2] [3iH-*, 4) _ ( 1)" + ' [2u+6, 5] [3u+6, S] 





( t)"[8,li ( l) +1 [2u+2,l][2iH-2,2] ( l)" + *[2m-4,2][2u+4,J] ( 1)" + S [2w+6, S][8u+6, 4] 

 H 1 



(-1)'"" 



{ 1)" [S, 0] ( 1)" + ' [2u+2, 1] [2u+2, 1] ( l)" + S [2tt+4,2][2w+4,2] ( 1)" + '[3M+6,31 [2u-t-6,3] 



o 



(-I)'" + "--,--,- COS . (3U)I 



*^/ T * 



(1)" * ' [2IH-2, 1] [SiH-3,0] (1)" + ' [2u-M, 2] [2u+4, 1] (1)" + 3 [2lM-6,3] [2u+6, 2] 



1)" * ' [8u-Hfc, 2] [2iH-*, 0] (-<)" * ' 



Etc., etc. 



4 A la place de (f). 



" * ' 1 'J!Ll LjL ^M-S, H . + 3 [2+S,2] . t [2p+2u- l 



cos., x * 2 



