of certain differential Expressions, &c. 
b ln z Zn . dz 
m 
the («+ i)th term =D"ii. =d” li. b (a»- 1) 7^ 
— D’ if 6'” x ( * v (i^~j~ )- Now, if the integrals of 
D" if 6*” (271 — 1) be taken and added together, for the se- 
veral values of n, (similarly to what has been already done,) there 
results, 
/=*{ Dlf . 6‘4-D 2 if . D1-*. 6 4 -f D 3 if .D* l“l b 6 + &C. } 
{ / - x +v/( 1 + 2, )-v^7?)} 
+ (4-) 
+ 4 1 } 
I.f.ai _£ r Z 6 | 5 1 3 •*» \ 
"I? b0 *V(l + « 2 ) l 6 6.4 T 6,^,2 J 
+ &C. 
consequently, putting z= f=, we have/(i) = of — 1 -J- 6 
= 2 (oiff + DMi .Dl-ifc 4 + D’ li .D- l-i.h 8 + &C.}{/.-i±^i± 
. 1 ) 
Vi -i-b J 
A/l-f b 
! r% tv* 1 — 
1 
-1- 2 JJ l2 
1 £ 
y/[i+b) ' 
2 
2D 3 if 
r , 
j * 
5& 3 
1 v/(i + 6 ) 
1 4 
4 • 2 
+ &c. 
the series Dif 6*-f-D I if . di“* 6 4 -j- Sec. numerically expressed, is 
+ — .-3-.6 4 -f ■■■I . ^ b 6 4- &c. 
2 '2.42 '2,4.62.4 1 
• This series is the same as 
— |D1 _ ^6 2 -f-Dl^.D* l"“H 4 -|-D 2 1“^.D 3 1^ 6® + &C. | 
H h 2 
