A new application methodology of the Fourier transform for rational approximation of the complex error function

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This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only 17 summation terms the obtained rational approximation of the complex error function provides the average accuracy 10⁻ ¹⁵ over the most domain of practical importance 0 ≤ x ≤ 40,000 and 10⁻ ⁴ ≤ y ≤ 10² required for the HITRAN-based spectroscopic applications. Since the rational approximation does not contain trigonometric or exponential functions dependent upon the input parameters x and y, it is rapid in computation. Such an example demonstrates that the considered methodology of the Fourier transform may be advantageous in practical applications.