I U f/.r=(- 1)"' ( V dx^ 



J c?.t''" J dx'>' 



r (i'«-iF dud"^-'^v d"^-w " 



U i 1- . .. -f(_iy«-i V 



|_ dr'" dx dx->^-- dx'"—^ 



thus, assuming 



and introducing the limits — oo and oo 



M 



00 



r d" 







or, adopting 



(_l)m L -x'^-0/+.r)^ Tl.J^n {U^X) dx 



00 



u = v\/2 



[/2 



00 



Applying now the relation (32), it is evident that the integral 

 reduces to the first term, thus 



1/2 (K2)'"+" 



or finally 



^^(_i).^ . nv/2; 



|/2 (1/2)'"+" 



16. We will now compare the preceding solution of the integral- 

 equation (31) with tlie formal solution given by Prof. K. Schwarzschild 

 Astr. Nachr. Bd. 185 N". 4422). 

 Putting 



t = e— ", s T= e—^ 

 the equation 



00 



f A (t . s) F (s) ds z= B (t) 



takes the form 



