R(r) = By + Bus, (5.91) 
L1, Mz being the roots of Eq. 5.73, Z) = Z*+a,Z +a =0. Bj, Bz are constants and are 
determined by the boundary conditions, as 
R(0)=02, R(1)= (a+ a2] o2. 
-—aj 2 
1l+a) 
Thus B,+Bz=02 and By; + Boz = 
2 
Therefore B,= Syl Bs a oe (5.92) 
(41 — 2) + ip2) 
2 Ou nae, 
= x: (5.93) 
(U2 —1)(1 + Wifl2) 
po) i 2 
Then R(r)= US LI i pe i o2. (5.94) 
(41 —M2)(1 + 412) (41 —M2)(1 + W142) 
If we need the expressiono¢ from Eq. 5.88 
(EN Ck SOSA 
1 +12 2 
pp eles eS ale 9 (5.95) 
(1 -wia(1—wi)(1 — 3)“ 
then 
R(r) = on ON eA 2 ae EA) Sienna ae eed ame a2. (5.96) 
(41 =n) wD — wea) “1” Gy — pad — wD — per) 
This equation is in the form of R(r) = By 4} +B by. 
There are a variety of cases in which, depending on the sign of 1), 42, the autoco- 
variance function appears different in its tendency. 
1. Whena2 < a?/4 (subzone [1] in Fig. 5.16), 41,442 are real, and 
a. if a, <0, aa>0 (region (1) in Fig. 5.16), “4; >0, uw2>0 
and R(r) stays positive as in Fig. 5.17(A), 
b. if a; <0, a2 <0 (region @) in Fig. 5.16), then 42), 42 have opposite 
signs, 
124 
