or 



X 



2<fi.v)=iB, ^^ +27?, ^ +(2i?„+7?,)/-2/?. fm ^-^^^^ d^i- 



il tV tl' rt/ «/ it/ *"^ iJ 



a- O 



o 

 Now pnlting 



rtj = 1 a^=z a^ = .. T= O 

 we have 



B, = l B, = B^ = l 7?3 = 7?, = ... + O 

 thus 



o 

 whic'li agrees with (10). 



Finally let the integral equation to be solved be 



X 



•^•= lq{i3)cos{x—l3)di3 







In this ease 



//g = 1 , r/i = , a^ = 2 , r/j = , r/, = 2 , . . . 

 thus 

 A, = 1 , .1. = , A, = 3 , .I3 = , .1^ = ^ , A, = , A,r=:4 ... 



and, aecording to (18) 





 wliicli. by means of the known relation 



/„(■'■) + 2/,(..)-f 2/, (.r)-f ... = l 

 may Ite written 



2^f{.v)=.2 +2J^d^ 



or 



^(.^•) = 1 + 1 



