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% cerfexp.m: Approximation for the function  (1-erf(x))*exp(x**2), used in pldf

% GUISDAP v.1.60 96-05-27 Copyright Asko Huuskonen and Markku Lehtinen

%

%

% Approximation for the function  (1-erf(x))*exp(x**2) with

% accuracy 1e-8 for all x.  Method: power series for

% erf(x) for small x, asymptotic continued fractions expansion

% for large x (Abramovitz-Stegun formula 7.1.14)

%                                             Markku Lehtinen 2.7.1979

%

% res=cerfexp(x)

%

  function res=cerfexp(x)

%

  x1=abs(x);

  sqx=x*x;

     if (x1<1.) 

        tail=0.;

        term=sqx*sqx/10.;

        erf=1.-sqx/3.+term;

        for n=3:12 

           term=-term*sqx*(2*n-1.)/(2*n+1.)/n;

           tail=tail+term;

        end 

        erf=(erf+tail)*x*2./sqrt(pi);

        res=(1-erf)*exp(sqx);

      else

        dum=0;

        for n=(55:-1:1) 

           dum=n/2/(dum+x1);

         end 

         res=1/(dum+x1)/sqrt(pi);

         if (x<0), res=2*exp(sqx)-res; end 

      end