Table 2. Cut-off points for determining the number of stages in the continued fractions. 



aber of Stages 



Real Argument 



X 



Program Test Value 



x3/2 



1 



10^ 



109 



2 



80 



715.0 



3 



35 



207.0 



4 



22 



103.0 



5 



13 



47.0 



6 



11 



36.4 



7 



9 



27.0 



8 



8 



22.6 



9 



7 



18.5 



10 



6.5 



16.6 



11 



6 



14.7 



12 



5.8 



14.0 



13 



5.5 



12.9 



14 



5.3 



12.2 



15 



5.1 



11.5 



16 



4.9 



10.8 



17 



4.5 



9.5 



18 



4.4 



9.2 



that gave equivalent accuracy for the two methods. Along 60° this minimum accuracy is 9 

 decimal places. 



The following relationship exists between hj and hj for positive and negative values 

 of the imaginary part of the arguments: 



hjCz*) = [h2(z)]* , 



where the * means complex conjugate. Thus, the above discussion at 60° can be translated 

 to -60°. Also, the functions actually need to be computed only in quadrants I and II. They 

 could then be evaluated in quadrants III and IV by the above relationship. The above rela- 

 tionship explains the symmetry of figure 4 about the real axis. 



33 



