A novel analytical solution of the deformed Doppler broadening function using the Kaniadakis distribution and the comparison of computational efficiencies with the numerical solution

This paper aims to present a new method for obtaining an analytical solution for the Kaniadakis Doppler broadening (KDB) function. Also, in this work, we report the computational efficiencies of this solution compared with the numerical one. The solution of the differential equation achieved in this paper is free of approximations and is, consequently, a more robust methodology for obtaining an analytical representation of ψ k . Moreover, the results show an improvement in efficiency using the analytical approximation, indicating that it may be helpful in different applications that require the calculation of the deformed Doppler broadening function.