A sampling-based approximation of the complex error function and its implementation without poles

Recently we developed a new sampling methodology based on incomplete cosine expansion of the sinc function and applied it in numerical integration in order to obtain a rational approximation for the complex error function w(z)=e−z2(1+2iπ∫0zet2dt), where z=x+iy. As a further development, in this work we show how this sampling-based rational approximation can be transformed into alternative form for efficient computation of the complex error function w(z) at smaller values of the imaginary argument y=Im[z]. Such an approach enables us to avoid poles in implementation and to cover the entire complex plain with high accuracy in a rapid algorithm. An optimized Matlab code utilizing only three rapid approximations is presented.