Partial Fraction Problem. 

 Adding to the second double summation 



Obo 



= (-l) 2 b a 2 (-l) a a a f , 2 2 n 



!+! k + 1 ^»- 2 -^ 

 2 / a 



K + l 



+ lj 



we finally obtain 



K + l 



"a - k+i-2/s 



Qs.+i-Sf-l)^ 2 (-l)Vm c+1 _ 2P . 



or 



p=o 



W. 



x[( a+ /)-(r + ?)(^>r/)^]. 



Q,. +1 = l o (-l)^(^+ 1 ) f (-l)v( a JJt )'»«*'-*-' ( 19 ) 



which is of the same form as (14). 



In a similar manner it can be shown that (14) holds also 

 for even values of k. 



It follows from (13) that A x is formed in the same way as 

 Qi»_3 (if it existed), therefore 



i ,. [ | ] (- 1 ). 4 .fi 1 )l*- i >-"-C^t I ) -.-' 



and 



[¥] 



n-2-2/3 



B,= 2, (-1)^(^0°) J o <-l)v( a J^)m„_ 2 - 2 ,. 



>■ (20) 



i (-D^f t 1 ) T^-^C^t 1 )— -j 



Continuing the process of division we arrive at 



Qi/c — Qt-iK — aQ,tK-i-~bQ tK -2i "J 



A^ = Q,;n-l-2^ — aQ,t + ln-2-2t — bQt+ln-3-2U / ■ (^1) 



B i =Q i _i K -aQ i(l -i~?>Qf (£ _2. j 



We now assume 



Q,^^-!)^^^ 1 )^^-!/^"^^ 1 )^^^ (22) 

 and show that this form holds for Q^+i, Qt+nc, and Q*+i K +i. 



