346 
PROFESSOR A. R. FORSYTH OR 
U\ 
AG+BH+"(AF+BD + CH) 
OC 
=^i+jW) sa y; 
^ w 2 x (Gr -(-/i H ) j 1 + ^ G 2 +yt 2 H 2 r 
= xVi(l+;p 2 ) say. 
Thus the n th term gives 
4(-l ) n tf 1 ^ A 2n-l 
-T4A C 1 1 - ~Pz 
2ji-1 Pl 
(2n—l)(X 1 2n ~+~ JL r^X 1 Z) ‘ 
-f > L2 ^„ 2 - 2 ^ - 3 (\ 1 ^+ ^ V- B 0(^i 8 +^ 1 v»)+ 
1.2.3 
B B"B_ [/ 0jt> n \x 2«—2.. 7~Z ~ n ^-- n '^-- n 4\ 2«-4,, 3 
Pl" 
- ; 2b - t ^ (2n-i)x^-Vi-^ 2 
1.24 
V*“Vi + 
4(—1)”A® r. 9„_, 79 2?i-2.25t-3, , 
14zr~i X i >2—^ - Y2 - Xf V 1 V 2 + 
PY 
2'7?_2 27?_2 2??_4- 
+ (255 - 2)X*-’V 1 - V - 5 Vi 3 + 
4( —1)”& S 
Pi 
2»—1 
- ^ (\ 1 +i ^ 1 ) 2 *- 1 - (x.-fiw*-* }+f{(x,+ iW’-H- (X, -ow*-*} 
X, 
■B^((G+^ i ) 2?J 3 — (Xi— ^Vr) 2 " 2 ] 
i denoting \/ — 1. Hence summing up for all the terms and reducing we have the 
whole coefficient equal to 
Now 
^k~{(pp—k~pp)(p,,p l — p l p^ x ) + \-(p, Pl + Pl p 2Pl ) — 2\\p lPl } 
(ft 2 + \*-JcW f + 4Jc%W 
Pl =G 3 +FH 3 
p^=2(FG+PDH), 
x 1= BG-ra, 
/ft=AG+BH 
P2=AF + BD+CH 
X,=CG + BF-FD 
and the values of A, B, C, D. H, F, G are determined by the seven equations 
Ac/^+B.qq, 
d~ H —Gs^ + Cc^+D d y — h — 1 
(j±— 1, 2, . . ., 7); and therefore the above is the value of 
