498 ON THE SUMMATION OF SERIES, 
Integrate, by parts, and we shall have, 
| . log. o(v) dx = @ log. o(v) — y log. o(y) — 
Y 
av 
| met . dw, and, by differentiating, we shall have 
log. ‘o(#) = TO and log. ‘o(y)= Tey 
Pat ae =o (7), -. ae =o (y). Substitute 
these values in equation (29) and it will become 
x y vee) | xv o(a)de+(A+a-+l) 
[)] = Lo(e)] xa y 
fo dx — (A+y+1) foun dy +B } o,(2) ue 
o(y)} +Dfo,() —0 (yt +F foi (e)—01 (yt +G 
fo, ()-0 (y)b+ &c., ve , where a may be 
any quantity whatever. ...... 25 LNa.enws (30) 
Since a may be taken equal to any quantity, 
let us make it successively equal to o(a) and o(y). 
