In these equations, the upper Value Is taken when S or G_ *,9 larger than and 

 equal to and the lower value Is teken when 0. or G>_ ie negative. In^lis and 

 Price have derived the Green function for a tranolating and puloating source 

 aliaiiar to G^ with the change of variable and with the change of Integral path. 



When the argucaent, -u.(z+i5) or ~u (s-l3) ie small, the exponential integral 

 can be expressed in a series forra (see Reference 10) as 



E^z) 



-y - In z 



J, 



<-Q n * n , 

 an! 



j arg i | < * (55) 



where z is any complex nusaber and y ** 0.577215? is Euler's constant. When the 

 arguaent becossss very large, the exponential integral is evaluated by the tnethod 

 of Todd. For a large complex number s «■ x + iy, the exponential Integral 

 Eultiplied with exponential function is expressed aa 



where 



e E^z) - Ij - il 2 



(56) 



2 2 

 (x + u) + y 



du 



(57) 



Io - 



x2 A 2 

 (x + u) + y 



du 



(58) 



17 



