80 Mr. Jarrett on Algebraic Notation. 



Put s — t — \ ; then 



/(r, t) ^ S:-' A„_,.,., .f{r+l-v, 1) + n' 

 Put t = »•, then 



w 



■r.f{r+l-t,l)...{3). 



m 



f{r,r) = Sr'A,,,_,.f{r+\-v, l) + rJ-' .^^- r ./ [l, l). 



r — 1, 1 

 HI 1 



But /(I, l)=lm_- 



•l^ 



»l "-r 7)1 



171 



= ?«.(;«— 1) .M.(w— l)=»i {/«- 1 -M+ 1} =»r. 



And «'-' 



- r .nr . 



= «'•+', 



m 



VI 



.-. f{r,r) =S:-\A,^.,.f{r+l -v,l) + n'^\\- (4) 



n 



r + l 



Again, /(r, 1) = {nr- 1) /(r, o) + {m-nr) ./(»•- I, o), 

 from (2), (5), 



1 l'« o. (-1)'"' , r + \—s.n 



and fir, o) = 7n --.'-. S% ^, '-— . r . 



'+' n 



, n- m „, (-1)'-' 1 



l!l lZL_ ^Izl » r+l-s.n- 



r+l 

 1 1 



m 



But 



nr - m 



r + l— s.M — OT rn — m r+\—s.n — m 



= -i-.{i+ ^^-^^" }; 

 wr-jw I r+l-s.w-m^ 



