Abel与pFq超几何微分方程之间的联系
A connection between Abel and pFq hypergeometric differential equations
摘要：
在最近的一篇论文中，我们提出了一类新的三参数Abel型方程，称为AIR，它的所有成员都可以映射到Riccati方程。文献中提出的Abel方程及其解大多属于AIR类。根据三次函数的根，有三种标准形式可以生成这个类。本文揭示了超几何函数2F1、1F1和0F1的标准形与微分方程之间的联系。这种连接提供了一个封闭形式的pFq解决方案的所有阿贝尔方程的AIR类。
英文摘要：
In a recent paper, a new 3-parameter class of Abel type equations, so-called AIR, all of whose members can be mapped into Riccati equations, is shown. Most of the Abel equations with solution presented in the literature belong to the AIR class. Three canonical forms were shown to generate this class, according to the roots of a cubic. In this paper, a connection between those canonical forms and the differential equations for the hypergeometric functions 2F1, 1F1 and 0F1 is unveiled. This connection provides a closed form pFq solution for all Abel equations of the AIR class.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
