SECT. VI.] VALUES OF THE COEFFICIENTS. 



are thus expressed, 



179 



a- A B 



- 



[7 



1T* 1 7T 6 1 7T 4 1 7T 2 



~ + - 



(7 



-lzL 6 ^!^ 4 l 772 ^ x&amp;gt; \ ^ 



[9 2 2 |7 + 2 4 [5&quot;&quot;2 6 |3 + 2V~ 



D^-lzL 4 ^!^..!^ 



Vg 3 2 |5 + 3 4 [3 3V 

 , F /7r_ 8 _^7r_ 6 ITT* j. 7r 2 . 



1-1 2 * 6 8 &quot; 



-D^.l^ 4 , l^.n 

 l7 4 2 5 + 4 4 3 4V 



|3 



&c. 



215. Knowing the values of a, b, c, d, e, &c., we can substitute 

 them in the proposed equation 



&amp;lt; (x) = a sin x + b sin 2# + c sin 3# + d sin 4;c + e sin ox + &c., 



and writing also instead of the quantities A, B, C, D, E, &c., their 



122 



