ÖFVERSIGT AF K. VETENSK.-AKAD. EÖRHANDLINGAR 1899, N:0 7. 685 



where 



^1 ~ 2 2 2 





^^1 



2 2 ■ 2 



r' 



(58) 



2 sin z 

 Thus by (22) and (24) we have 



1 



TO = 1 ( TO=1 



m + 1 j-j m — 1 



+ G™ 



»I + 1 »J + 1 



Sin — 5:^ — 7„ cos — ö — "-^ 



<i) f »^ 



sin- X 



■ m + 1 ■ m + 1 



Sin — 7: — X sm — ?i — '/. 



sin- X 



+ 7^(2) 



+ a 



sin 



X cos ■ 



sin-x 



m — 1 . 7?i + 1 



sm • — jr — X sm — s — y^ 



(•:) 2 2 



sin- X 



(59) 



By introducing the expressions (49) and (59) in (52) we get 



m 



2^ S,n = m{S^ + To) + H,- — ^— + ^2-— 2 — + 



:i(l) 



sin 



: + l 



+ (i^;'^— ^1 sinx) 



771 + 1 



X COS -^— X 



+ (7^2)_j^_sinx)^ 



+ (G^f— -S^sinx) 



sm- X 



- 1 9« + 1 



— X COS ^^— X 



+ 



sm- X 



TO + 1 . TO + 1 



sin ^^— X sin ^^— X 



+ 



+ ((y^^^^_^^sinx) 



sin- X 



. m — 1 . m + 1 



Sin — - — X sin —;t— X 



-f 



(60) 



wliich is the expression sought for 2j ^m • 



m = l 



By (44), (45), (49) and (60) now the equation (20) for K„, 

 will become 



