492 On the Expansion of a Function. 



i ' x co 1 p-l / K a—1 1 \ 



= 0+i)i| 2 ?— - — , n( s »- t o) 





= (p + l) ! ^ (-l)»a*»f- 4 ( 2 9 , J 



r J J m =2 K \ KO =i^o+^-2/ 



x n ( 2 :> , 9 )*»» 



a 



co r 2»i+j?-l / m 1 \ 



Replacing m by /e and /c a _i by a:« we obtain 



oo r 2K + p + l-2 KO 1 



oo r 2 Ko +^+l-2 



p+l_l K i -j^ x 



which is of the same form as the expression (I), p being- 

 replaced by p+1. Hence reasoning by induction (4) is 



true for all positive values of p. 

 o 

 Therefore assuming II A a =l, we have 



a=l 

 oo r 2K + p-2 p-l/ K a-l 1 \ 



