pa 



( 227 ) 



4 ' 1— ;> 2 



Jt was in looking for a way to place in a form of a dclinitc 

 integral the general term of the series of IjAIMBEHt modiiied by 

 Clausen : 



00 



l+.t"» ., 4 rsbi a cos {n-\-l) a da 

 l-f.f'*"'' ~ JT J 1 — 2. c" cos ((-{-. V-" « 







that I fonnd this error. 



It is easily seen that the i-ectitieation has to be extended to the 

 whole N°. 12 of tlie method 41 of whicli the above mentioned 

 integral forms a part and to any other a})pHeation of the general 

 formulae of page 134. 



This paper was given to Dr. J. C. Ki.uyveu, who made the follow- 

 ing communication about it: 



The remarks of Mr. Williot are on the whole correct. In tlie 

 "Exposé de la Theorie etc." of Bierens de Haan we really find on 

 page 639 



a 



siti X cos ax ct i)^~^ 



dx—- ' 



1 2pC0SxA;-lf' X 2 1 p 



\—p 



and this is incorrect whether a is an entire number or not. 

 Mr. Williot now gives as an answer 



T 



and tluvt will do for a as an entire number. 



Ill the meanwhile he might have observed that this resuk neither 

 holds good for a, (not an entire number) and that Ave tind for any 

 possible positive a : 



Jt pin—^li -l-y>["+'1 



7^<1 



4 * l—p 



Jt /)-[«— °] -\- 27-["+o1 



;> ^ 1 : — . 



^^ 4 p{p-\) 



(Here [(t\ means the greatest entire number smaller than it). 



(October 27, 1903). 



