1517 
where 
ys r*/(cr+ By) (70) 
The general solution of this equation is: 
P= Aly) pF) + Bi) exp (bx) (71) 
The functions A and B are to be determined from the boundary 
conditions. 
8.2 The function 4 ¢/ Cerys is 
e = Ey VE 
has a branch point in the complex y ~Plane (Fig. 6) at fe ~3c*/4y, 
From this branch point, a cut is made to = — 60, The upper 
sheet of the Riemann surface so formed is chosen so that b is 
real and positive if ye is real and greater than -30* /4v ‘ 
The integration in equation (65) will be taken on the upper sheet 
of the surface. The integrand of (66) is: 
Aly) exp (¢t- x) + By) exp(ytrbx) 
For x 7 0, the second term becomes ae as 1 ms Cos Gaon, 
since Re (yt+ bx) —> ol + Giri/ev)” x —> +00. The 
first term approaches zero strongly because 
2 
Re (gt - bt) a of -(3/t//8 vy x ~- ©. 
We accordingly set B = 0, and obtain A from the conditions at 
X= 0: 
Ar) [otorlepert aa , (72) 
analytic for Re [> oc 
a) GL oe 
