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 ${\psi }_k$. 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.

中文翻译：

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使用 Kaniadakis 分布的变形多普勒展宽函数的新解析解以及计算效率与数值解的比较

本文旨在提出一种获得 Kaniadakis 多普勒展宽 (KDB) 函数解析解的新方法。此外，在这项工作中，我们报告了该解决方案与数值解决方案相比的计算效率。本文获得的微分方程的解没有近似值，因此是一种更稳健的方法来获得解析表示${\psi }_{ķ}$. 此外，结果表明使用解析近似可以提高效率，这表明它可能对需要计算变形多普勒展宽函数的不同应用有所帮助。