论文标题
Julia中的小聚糖函数
The Polylogarithm Function in Julia
论文作者
论文摘要
小聚集函数是重要数学函数的星座之一。它具有悠久的历史，并且与其他特殊功能和系列的许多连接以及许多应用程序，例如在统计物理学中。但是，其数值评估的实际方面尚未收到其兄弟姐妹对综合治疗的类型。只有少数正式出版物考虑对功能的评估，并且最关注特定领域和/或假定任意精度算术的关注。很少有文献包含对数值性能的任何形式验证。在本文中，我们提出了一种用于计算复杂参数和参数的聚类的算法，并与Mathematica中的任意精度实现进行了彻底评估。该实现是在一种新的科学计算语言朱莉娅（Julia）中创建的，这是该目的的理想选择，但也允许我们以简单，自然的方式编写代码，从而使其易于将实现移植到其他此类语言。
The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics. However, the practical aspects of its numerical evaluation have not received the type of comprehensive treatments lavished on its siblings. Only a handful of formal publications consider the evaluation of the function, and most focus on a specific domain and/or presume arbitrary precision arithmetic will be used. And very little of the literature contains any formal validation of numerical performance. In this paper we present an algorithm for calculating polylogarithms for both complex parameter and argument and evaluate it thoroughly in comparison to the arbitrary precision implementation in Mathematica. The implementation was created in a new scientific computing language Julia, which is ideal for the purpose, but also allows us to write the code in a simple, natural manner so as to make it easy to port the implementation to other such languages.
