Al. a. Tchouproff 
189 
Eiit 
/=0 g=0 
2/+ 2 
H'r+f-g H'r-2-j'+g 
(iV- (N- 2f''"'^"*- (*T^)' 
= iV>,- - + 2C,' + /a/] - - 26V- + ^^-r-l^ M 
- 3C/ /l,2 - 2C/ CS._i [fJ,r /J'r--2 + /*"r-i] /^s 
— 2Gj.- CV_2 [Mr+1 + + S/^Vl] f^i — 14<C/ /Xj.-o jX^ 
Substituting in (11) and replacing v-2r,{N) in (11) by its value in terms of the 
yu.'s by formula (4), we find after reduction : 
+ ;U,>_i /lia + r (r -I) fir Ata} 
- ] 2r/i2^ - r (2r- 1) /z.2^_2 yu,, - 4?->,+i - ?-(3i- + 1) /x/ - r(j- - l)fir+-2 f^r-i 
* ! 
+ 3?-'/tV_iyU,2 + ?•('•- 1) (4?-+ l)/irAtr-2/"2+''' /^c-s ■ !-(12), 
+ (r-1) /J,r-i f^r~2 f^f. ' 
+ -g- /"r At;; - f r" (?• - 1 /Li%_., /to' - (v - 1) (v - 2) /X^-i l^r-i l^i 
and hence 
|2 - r (2 r - 1 ) fj.^r_. ix^-rir-l) fi^+i /u-r-2 - 4r- fir+i fir-x 
+ yLty+j /tr_3 /i2 j 
- (r - 1 ) (r - 2) fi,_, fj,,_, fi.^ - /i-V-2 j + • • • j 
.(13). 
