a Plate exposed to a Beam of X-rays. 211 



To reduce the remaining integrals I consider the following 

 functions : 



*w=J o m dt > (7) 



<t> m (^)= J (l_f_£)m> ( 8 ) 



{?n an entire number). 



It is readily shown that the subsequent expressions hold : 



*&=££**- (9) 



4>(\)=A~ e -^dt, (io) 



^,„(X)=X»^f"^pA, . . . (11) 



^( 9 \)=\-»-if (0ir dL ■ ■ ■ ( 12 > 



These will be employed below. </> m (\) may by partial 

 integration be reduced to </>(X). By simple calculation we 

 get 



fl»(\)= l / J * »(X)+ X , 7 ^ * ?v . (13 j 



(7)1 — 1)1 v=o(^ — 1) [m — v — l) v ' 



I am now going to show r that the integrals found in K of 

 the form 



1 (lW^ 



may be reduced to expressions which only contain the 

 function <£ together with rational functions of z and k. I 



therefore examine the integral 



C z <? _&c r°° e~ kx 



J (i+5)= -*»<*> -J, <r^r^- 



I put t + z = x and get 



C z e _kx r w «~ 4 ' 



J. (IW^^-^1 (1+M^ 

 But according to (12) 



