ÖFVERSIGT AF K. VETENSK.-AKAD. FÖRHANDLINGAR 1899, N:0 7. 681 



where 



0^= A^{c) sm (e + y.) — A^{s) cos (& + •/.) — Ai{c) sine +Ai{s)co&e ] ^ ' 

 V^=A^{c)cos{ß + y) + A2{s) sm (6 + y.)-~ A i{g) cos 6 — Ay{s) s\r\d ] ' 



If all indices in tlie right member of OD or f" cbange, this 

 is expressed by resp. 0^ ^"'^ ^^2- 



By summation of the right members of (34) and (o5) with 

 respect to i ^ye get resp. 



C,a — C _i = — (— 1)'» [<D,(^0 cos 7nx — W^iic) sin my.'] . . (37) 



and 



Cm — Cn -1 = ^1(9) COS wr/, + 0^(g) sin my . . . (38) 



where for odd i 



+ °° i+i 



2(— 1) ' a)(0 = -CD( + l)+CP( + 3)-(P( + 5)+ ... 



i= — CO 



+ 0(- 1) - 0(- 3) + 0{- b)-...='0{u) (39) 



and for even i^ 



+ 00 ^ 



2(— l)2a)(0 = — (Z>(+ 2)+0{+ 4)— CP(+ 6)+ ... 



. _ö)(_2)+a)(— 4)— ©(— 6)+...= Ö>((7) (40) 



and analogous for W and A and thus 



Ö>i(^) = ^2(^ c) sin (ö + 7:) — ^2(? s) cos (ö + x) - 



— ^iCc) sin 6» + Äj^ils) cos 6» 

 ifiG) = A^il c) cos (ö + z) + ^oC; .^) sin (ö + ^) - 



— ^j('(^c) cos (9 — A^ds) sine. 



(41) 



By summation of (37) and (38) from ?n=l to ?« = m with 

 regard taken to the formulas (22)— (29) we have resp. for odd i 



2(an-C_i)= + 0,(u) 



• m + 1 m + 1 



Sin — Ti — y cos — 7^ — y 



sin y 



7)1 — 1 m + 1 



Sin — K — y cos — ^ — y 

 ®o(w) 



sin X 



This formula is coutinued on the following page 



