838 
ax,” log « 
= + O(«#,"—'! log x) 
mn 
au, n 
EK ara 
u=2 
az,” ine a £—1 yn ally nl 
— PENS en 
mn MN u=2 U == ae 
ax,” log x : 
= ————_ + 0 («7-1 log z) 
mn 
a 
— — fa," log « + O(a," log x)} + O (#,"— log 2) 
mn 
= 0 (a,"~-1log 2). 
Lemma. Suppose that the function #, has m and n, as para- 
meters and f, as corresponding function and that /’, has m and n, 
as parameters and /, as corresponding function. If the formula (1) 
holds good for n =n, and for n =n,, we have 
1 1 
7 n lga—1l (as am 0 lg —2 
Sede ag TO | OP 
dd, < x hn, ‘ny ! log oe vl 1 log x ; 
d,d, =l vam=l v m 
1 being prime to /; in this relation /(v) has been substituted for 
the formula 
v 
wf HAS A 
d 3 Ji ( EA (5) 
Proof. Let /, and /, be two integers, prime to 4; it follows from 
the identity deduced in the preceding paragraph that 
Sr B) FIT TE en 
dd, <a 
d,=1, 
d,=l, 
where 
Ee 
jf ea (d,) p> F, (d,) 
d=1 ds=1 
dek ik 
bah 
Va 
T,= = F,(,) = F,@); 
d= d,=1 
do—l. dl 
te 
Ti. Srey 
dit 
