MR. E. AT. BAEXES ON THE THEORY OF THE 
.3 6 (A 
and, tliereidre, on integration, 
log r.T {z “|- ct I oj.^^dz = 
o'" 
log Fj (a 1 (On) da + a log (coo) 
ruj, 
+ 2 r}nTL {a j co., ) + log I (0|, (O.n )dz. 
. A 
* 0 
§ 73 . We proceed to evaluate the constant term 
log Fn {z i coi, (On) dz 
by an application ol the multiplication theory for the case m = 2. 
We have 
[ log Fj { 2 z) dz = ^ [ log Fo {z) dz, 
Jo "" ““Jo 
and therefore, by § 65 , 
J 0 
(O: 
log r, (z) + log Fo ( S 4 ) + log F3 {z + 'Jy) + log Fo ( 2 + ^ 
/ 
^ / 
— 3 log po (coj, (On) — oS/ (22) log 2 + 3 (m + m') 27 tl gS/ (0 
= 1 [ 'dz\ 2 log Fo( 2) - log Fi(2 j C02) + log Pi ((Oo) + 2m7rt Si'(21 coo) • . 
Put a = |(Oi, l^coo, and i ("1 + (On) successively in the formula which we have just 
obtained for log Fo (2 + a) dz. and substitute in the formula just written. We 
Jo 
obtain 
sf log Fo( 2 )c 72 
J n 
j + j “ +1 " ~ 2 J [log hi (2 I (1)2) dz] — i-j + cao j log Pi(w3) 
+ 2m7TL 
((Ui I (On) — Sd I OJo ) — Si ( I (Oo ) — Si 
(Oj + COo I 
(o.^ 
+ 3 ct»i log po(ct)i, (iJo) + ■^oSi(2ci»i^ log 2 — + m^) 27 rioSi^(o). 
By means of the formula 
log hi {a I C(j) da = a log Fi [a j co) — Si (« | co) + (o log 
Fi(f( + (01 ft)) 
Pi(") 
