130 Dr. Brinkley's Investigation of the general Term 
h 
2 . 
b — \b \h 
e —i e — i e z +i 
( 3 ) 
Let p, q , r, and 5 represent the coefficients of A 
W2+I 
in the expansion of -g~~> ~Tb — ’ ~ and -——respectively: 
e_xe z _ie+j e 2 -|- 1 
then it is easy to see that -~—^-=q, —■ ■ r -j =s and therefore by 
2 2 
equation ( 3 ) p=q—s=^r . , 0 r p-. 
1—2 
m -\- 1 
To obtain r the coefficient of in the expansion of 
A (2+ -f &c.)- F 
Let^ (l) = i w 
<^ 2 ^ =y°| where =2 and pt-\-qv =m 
=/"( Tj* (1?)^ (i r j w where andy>/-f-<p-{“ 
-j-rw=w 
&c. &c. * &c. 
Then the coefficient of h m in the expansion of 
( 24-/2+— + &c. ) *= 
-^ (0 +^ W -^ (3) +&c. 
But by Lemma I. 
d = A 0 
1.2 = A 2 o W 
1.2.3 = A 3 ^^ 
&c. &c. 
Hence the coefficient of h m+1 in the expansion of orco- 
0 —i 
