Al, a. TCIIOUPROFF 
167 
t-k {ov2!-f+l,) 
n 
(2/) 
1=1 f,(f-!'-+n firf^/J-r,,---!^,-,-^^ 
- 1 fi s\-l)^-/:J.3,-_,+,-a- 
i. (1) ^ k = 0 
(or 2i-l-i-lk) 
X S 2 
7 = 1 f,(t-k + l) M;y^ ■ • • H-rf^ 
y, (2) '1 ■'2 /, =U 
(-/,:( or 2/- 2 - ; + /i- ) 1 1 i-2i) / A^,- ,. • 
X 2 2 
7 = 1 /, (i-k + 1) f^iy^ /^,y., • ■ • ^/y^_^ 
7-1 
+ (-!/' 2 u 2 (-l)^^.;_,+i.-/a■ 
./, (70 ^1 'h k = (> 
7 - A- (or 2;- A - 7 f 7. ) H (-27) / /A,- . . • • • f^,- , 
X 2 2 A^/''i • '>2' 
7 = 1 /, (7-A+7) /^'/, /^'■//••/^'V^_,^, 
4 (- 1 f'-'-^ 2 M., ■ • • l^r;, 2' (- 1 /3,+, ,, 
.y, (27-7-1) -'1 ■'2 ''at-i-l /, = o 
7-/,- (or/,+1) n,2/,/yU, /X .../X 
X 2 2 ' /f/'-'i- '•'2. 
7 = 1 /, (7-7,+7) f^r, I^Vf ■■•l^r, 
■1 '2 't-k+l J 
where the summation foi" / extends to all positive integer values of / from 1 to the 
least of the upper limits. 
By the aid of simple transformations the coefficient of l/iV in the development 
of can be expressed in the form : 
...(17: 
7( = (l 
7-1 7-7,- 
+ 2 (-1^-2 2 
k = Eiit. (7/2) / - 1 ./, (7 - 7,' + 7) H'rf^ /^jy., • • • l^ff^ 
li-f-) 
7/=0 
Eiit.(7/2)-l k + l 
+ 2' (-ly 2 ^ 
/c = 0 
= i,/;(7-.+7, ^,,^/x,.^...M,.^_^^ 
7r/':7,.'7.,...'v,^,) 
x"2'\-l)'' CK,_uk-il3„^f+k-,,,k 
t-2k-2 
Ent. (7/2) -1 
+ 2 (-ly 2 
* = 0 
n 
(2i) 
.(18). 
X 2 (-l)"CV,,^,,+;/3,,.,^,_,,,, I 
