( '^ ) 



and EF the arc of the curve 



As according to § 3 in tliis closed region and on ihe boundary 

 the function to be integrated is regular, the Cauchy theorem furnishes 

 for the integral appearing in (14) 



J ■^M,Us).,=J = f+J+J+J+J . . (15, 



2—xn AD AF FE ED DC CB 



Now I have proved in § 10 of my i)aper on the arithmetic 



A'* 

 progression for a certain function K{s) that, when integrating — /v(ó) 



along ihe same given path, we have 



AF FE ED DC CB 



where c denotes a positive constant^). Concerning that function K{:i) 

 I have made use 1. c. only of the fact that it is regular on the path 



of inteiiration and satisfies for < > 3, 1 — ^ <? ^ 2 the inequality 



" — log'^ t — — 



As now according to (13) the function Mi,h{^) has exactly these 

 properties, we have for the present case the expression (15) 



c 



/ -Vtogx\ 

 ^=1 0\xe 1. 



This gives after substitution in (14) 



X 



Y^l,{k)log-^^oLe-^^^'^ (16) 



l—\ 

 \ 6. Just as in § 4 of my paper on the function ix{h) it could be 

 concluded from 



X 11 



that 



1) May be c=3a. 



^^{k)log- = 0\xe 1 



