论文标题
不完整的麦克唐纳功能的基本属性与应用程序
Basic properties of incomplete Macdonald function with applications
论文作者
论文摘要
MacDonald功能的不完整版本在文献中具有各种称呼，并获得了当之无愧的计算挑战的声誉。本文将以前的不相交文献联系在一起，并介绍了不完整的麦克唐纳函数的基本特性，例如复发和差异关系，序列和渐近扩张。本文还表明，作为简单的封闭形式表达的不完整的麦克唐纳函数是抛物线偏微分方程的特殊解决方案，该方程自然而然地以多种瞬时和扩散相关的现象出现。
The incomplete version of the Macdonald function has various appellations in literature and earns a well-deserved reputation of being a computational challenge. This paper ties together the previously disjoint literature and presents the basic properties of the incomplete Macdonald function, such as recurrence and differential relations, series and asymptotic expansions. This paper also shows that the incomplete Macdonald function, as a simple closed-form expression, is a particular solution to a parabolic partial differential equation, which arises naturally in a wide variety of transient and diffusion-related phenomena.
