EXPLANATION FILE OF PROGRAM CMPLXSER
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  Complex Series
  --------------

    Once the coefficients of the approximating polynomial of a function f(x)

  have been found, the results can easily be extended into the complex plane 


       P(Z) = a  + a Z + a Z^2 + ...    where Z = x + iy    (2.9.1) 
               0    1     2

  This can be accomplished by employing a few of the complex algebra subroutines 

  in the first volume of BASIC Scientific Subroutines. The result is the complex 

  evaluation program CMPLXSER. This program uses three other routines concerning

  complex numbers.
   
    The inputs to CMPLXSER are the degree of the polynomial (M), the corres-

  ponding coefficients [A(i); real), and the real and imaginary parts of the

  argument (X and Y respectively). The result of the summation is returned in

  two parts, a real (Z1) and an irnaginary (Z2) component.
   
    As you can see from the examples given, program CMPLXSER is easy to use and

  has good round-off error properties.
   
    CMPLXSER can be employed to very effectively extend the application of the 

  computer to the evaluation of functions having cornplex arguments.


  From [BIBLI 01].
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End of file Cmplxser.txt