AND ON DEFINITE INTEGRATION. 489 
Hence equation (15) will become 
ile 1 oe 4y—1 
eM one 4a — ye (log. Ax— — log. a 
1 l 1 1 1 
sar, Ores o Ar—i — (Ay —3 + on 
1 1 l l 1 
3 eee (42-1? ~~ (4y—3)? s fae) + 
Bash ipeetr ca, 2 ply Sy CaaS Lhe | 
Be ( (42—3) (4¢-1) (4y—3)! aE Ta f, 
4 1 Lilt bt Este 
63 t= ~ (42-1) = (4y—3)° : Tei) ‘A 
Be ee tk UY Worle fee | 
15 aes (4x—-1)® (4y—3)® § (4y—1)° 
48 1 1] 1 i 
Slgaee 7 (42—1)" fe (4y—3)"* (4y— | a= &c., 
CES Seen Lonivincltd aliclabeasanesih Caene as (20) 
The complement of the definite integral 
1 a LE oe ‘dl 
; ee —Gpr ) 2% converges very rapidly 
when « and y are large numbers. 
If in equation (20) we take 2 = infinity, we 
shall have 
3T 
