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BELL SYSTEM TECHNICAL JOURNAL 



Instead of dealing with W(f) it is more convenient to deal with (47rV)~^ 

 W(f) which is the sum of the three components 



2\/Tr n=l 



-3/2^-/2/ (4n«r2) 



(47rV)-V2(/) 



(1 - e-f>y (f 



•V27r 



?'e)"--"- 



(8.12) 



(4: 



1 r°° 



■'oT'W^Xf) = - / Z{u) cos (m//(7) du 

 X Jo 



0.08 



0.07 



0.06 



0.05 



0-04 



0.03 



0.02 



0.01 



f/o- 

 Fig. 9— Approach of H^(/) to limiting form. 

 As p -> 00 , W{f) -> 4xV (p V2^)-i (//<r)2 exp [ - P/{2a'')]. 



The integral involving Z{u) has been computed by Simpson's rule, yi and 

 y2 being obtained from Table 3, with the results shown in the first section 

 of Table 4. The value of Wiij) may be computed directly, and lFi(/) may 

 be obtained from Wsif). The values of these two functions together with 

 those of Wz (J) enable us to compute the values of (47rV)-ilF(/') given in 

 Table 4 and plotted in Fig. 8. 



Since, as is shown by (8.9), Wn{J) varies as 1// for large values of/, the 

 areas under the curves of Fig. 8 become infinite. This agrees with the fact 

 that the mean square value of 0' is infinite. 



The values of (4irV)-' 14^(0) for p equal to 0, .5, 1, 2, and 5 are .7369, 4118, 

 2322, .07529, and .003017 respectively. When these values are plotted on 



