SOLUTION OF THE DIFFERENTIAL RESOLVENT. 297 



The general term of this is 



/13 25 37 i2m+i\ /lo 22 34 12m — 2\ 

 \ ± ' 4- ' A- ' " 4 / \4- ' 4- ' A- " ' 4 / 



5. 8.... 3m + 2 4 . 7 . 10 . . . . 3m+ I 



/7 19 31 i2m-s\ 



U ' 4 ' 4 • • • 4 4 -- 

 3 . 6 . 9 ... 3m 



The reader who will attentively examine this expression, 

 will see that it can be transformed into 



7 10 13 16 19 22 25 28 I2m+i 



4 4 4 4 4 4 4 4 4 _ ,«. 



(3-4.5 •••3^ + 2) . (4.7.io...3m-2) 



= C^3™ . 



^m-i p(-^^_j_^^ .nm + -j 



3^ 

 (where C is a certain irrelevant factor) 



44W * ~ 



Now we know that 



.«■ J 44"* _ / i\ 



'(3^ + 2)^ mH — ) 



IT 



s-h .a (n h\-a '^ Via + b—i) 



Hence we shall have 



r(3m + 2)r(m + ^) TT J _!r 



whence we obtain as the sum of the series, . 



p ^ ^l cos^^ j cos ^ -cos^^ cos- . ^^ I 



^AdccccY dd 1 ^-- ^ .\J . 



"" ^ J -I I _ cos4^ COS 2e(^j + cos^^ i^ 



