( 204 ) 



case somewhat intricate. By repeated difFerentiations it is derived 

 Ironi /( .V, — J, for we have 



^ = 1 * V 2y r(|) * V ^ J 



./ i\ 1 



To evaluate / I ■/% — - 1, we put m z= -^ -\- ö in the general expres- 

 sion for ƒ(.(', 7/0, and make ö tend to zero. In this way we get 



/)= 00 





,2// 



h = ' 



We shall now pass on to consider the second integral 



00 



ƒ sin xt 

 dt , 







and it will appear that its character is (püte similar to that of the first. 

 Again wc transform the integral l»y the aid of the identify 







QC 0(j 



r{iii) if) (./•, ;/t) := I c— " iC" — I ^/« I 6' - "'' .5in .rf (7«. 

 u 



A further transformation .i»ives 



1 „ 1 



and obtain 



fe '''%ln.ctdt = ^ Ce -i"^^ ''^/i^z-^/t' ■!« (! — »•) '2 



x^w 1 







and therefore 



(1_,,.) 2 ,/,,. I ^. " ~^ n"~' da. 

 fi 



Comparing this equation with the equality obtained before 



