496 



:-y, 00 00 



1-^f o nf\l-\-tJ J l-\rt o w/ J l+< 



o 

 or 



dt = e-j ^^JA2\/.vt)dt ... (15) 



o o 



In order to deduce some more relations from formula (11) we set 

 to work as follows. In Dr. Nij]-and's dissertation ^) the following- 

 relation is deduced for Abel's poijnomia: 



n— 1 

 ffn' {■<■) = — 2 (/k (*•) . 



By summation of formula (11) from n = to n — 1 : 



00 00 



ƒ»-! pi f g—t n-1 

 e-i 2 dt = 2 (pn it) dt 







or 



ƒ1 t» ] re-f 

 e-i 1 dt:= I Wn' (t) dt 







or 



00 -" 



J (HI)" J 1 + /^^^ 







We integrate the second member partially : 



00 00 



(/,/ (0 df = (f,, (t) ^ + ^ ^ e-hfn (f) dt 







00 00 



r/ „ (/,) dt -\- I ■ (/,^ (t) dt 



= - 1 + 







Formula (16) passes into: 



00 00 00 



r t" Ce-i r e-t 



I e— ' dt =z I (ihXt)dt+ I (In {t\ dt 



J (1+0" Ji+^^^ J (1+0^ '^ 







or by application of (11): 



1) Over een bijzondere soort van geheele funcliën. Utrecht. 1896 p. 19. 



