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

Abstract

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 $0\le x\le 40,000$ and $10^{-4}\le y\le 10^2$ 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.

18 pages, 3 figures

References in corpus (5)

• Decay time integrals in neutral meson mixing and their efficient evaluation
• Sampling by incomplete cosine expansion of the sinc function: application to the Voigt/complex error function
• Accurate approximations for the complex error function with small imaginary argument
• A rational approximation for the Dawson's integral of real argument
• Representation of the Fourier transform as a weighted sum of the complex error functions

Cited by in corpus (2)

• A rational approximation of the Dawson's integral for efficient computation of the complex error function
• Efficient application of the Voigt functions in the Fourier transform