SECT. VI.] DETERMINATION OF THE COEFFICIENTS. 177 



+ 12 02 + -1 2 A9 + 92 02+02 J2 + 02 42 + & ( 

 J. . O l.T) Zi . O Zi.rr O.T 



!&c 

 I 2 . 2 2 . 3* I 2 . 2 2 . 4* I 2 . 3 2 . 4 2 2 2 . 3 2 . 4 2 



1 2 .2 2 .3 2 .4 2 2*.3 2 .4 2 .5 2 F.2 2 .3 2 .5 2 &amp;gt; 

 by P, Q, 5, 5, &c. 



aj 3 x 5 x 7 

 The series sin# = # s + j^ ?= + &c. 



3 |o 7 



furnishes the values of the quantities P, Q, E, S, &c. In fact, the 

 value of the sine being expressed by the equation 



we have 



1 -g + |-| +&ft 



Whence we conclude at once that 





213. Suppose now that P w , Q B , 5 B , /Sf n , &c., represent the 

 sums of the different products which can be made with the 



fractions 2 , ^ , ^ , -^ , ^ , &c., from which the fraction -= 



Z o TC O 71, 



has been removed, n being any integer whatever ; it is required 

 to determine P n , Q n , E n , S n , &c., by means of P, Q, E, S, &c. If 

 we denote by 



the products of the factors 

 1- 



V 



\ H. 



