DE QUATRE FONCTIONS. 25 



En changeant les puissances des sinus, en sinus des arcs multiples, il vient : 



(VIII). 



lu + I 1 



* ( [3u+l,u] [2iM-5,iH-l] [2iH-S,u-+-3'j[8iM-S,21 [2j)+2- 1 , p-t-u i] [2p+2 i,p- 1) 



(_l)"[2it-H,3] ( 1)" * ' F21H-3, 1] [2iH-5,4] (1)" * 2 [2i(+S,2][2u+5,] ( 1)* +3 [2li-4-7, 3] [2u+7,6] 

 + 8 



(_l)"[SiH-l,a] (-1)" + '[211-4-5, 1] [3+5, 3] ( 1)" * [2+S, 2] [2i(H-5, 4] (-1)"* [2iH-7,3] [2M+7.5] 



s . n 



;-!)' [211+1,1] (-l)* + '[2B-H5,l][2iH-g,2; _ (-1)' + ' [2iH-5, 8] [2IH-S, 5] (-1)" + 5 2'M-7,5] [2it+7,*J 

 *+' " + <* + ' 



\ sin. (2 1 



(1)" [2-H,0] (<)"* *[2lH-3,l][2iH-5,l] _^_ ( J)''' l ''[3iH-S,3][3iH-S,2] _ (-1)* * 3 [2<H-7,3] [3n+7,S] + _ 



'^^"T^C 1 " 2 ^ 2 '" 1 '^^ - ! sin - ( * H - 1) 



., t][2iH-3,0] (- 1) " * * [21H-S, 2] [3<H-S, 1 ] (-1)" + 5 [2lH-7,5l [2-4-7,2] 



s . n 



(-1)" t '[2u+B,2] [2u+S,0] _ (-<)* 3 [2u+7,3][2iH-7,l] 



s|n 



(- 1)" + ' (2U-+-7, 3] [am-7,0] 



sin. (2IH-7) - 

 Etc. 



FIN. 



