492 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1954 



behave in much the same way as those just described. The Hne nir = 

 divides the m-plane into two regions corresponding to different types of 

 paths, and the negative real axis is a line of zeros corresponding to 

 Re U(ii) - J{k exp {-2-Ki))] = where ii = m is the saddle point. 



11. I w I = 0.55p^ arg m = it. Fig. 11.6 (a). This value of m marks a 

 change in the type of path. 



12. \m\ = p^ arg m = ir. Fig. 11.6 (b). 



13. 1 m I = p\ arg m = 7r/2, arg {ip~ - 2m,) = 37r/2. Fig. 11.6 (c). 

 The complication of the paths in Fig. 11.6 (c) is due to the superposi- 

 tion of two boundaries in the m-plane. Im f(to) = Im f(h) accounts for 



ARG (Z^ -2m) = 375/2 



Fig. 11.6 — Paths of steepest descent for miscellaneous values of m with z - 



i^'^p. 



