The method of Frobenius is a standard technique to construct series solutions of an ordinary linear differential equation around a regular singular point. In the classical case, when the roots of the indicial polynomial are separated by an integer, logarithmic solutions can be constructed by means of perturbation of a root. The method for a regular [Formula: see text]-hypergeometric system is a theme of the book by Saito, Sturmfels and Takayama. Whereas they perturbed a parameter vector to obtain logarithmic [Formula: see text]-hypergeometric series solutions, we adopt a different perturbation in this paper.

中文翻译：

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对数 A-超几何级数

Frobenius 方法是一种标准技术，用于构造围绕规则奇异点的常线性微分方程的级数解。在经典情况下，当指示多项式的根被一个整数分开时，可以通过根的扰动来构造对数解。正则[公式：见正文]-超几何系统的方法是 Saito、Sturmfels 和 Takayama 著作的主题。尽管他们扰动了参数向量以获得对数[公式：见文本]-超几何级数解，但我们在本文中采用了不同的扰动。