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Logarithmic $A$ -hypergeometric series

Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan

E-mail Address: saito@math.sci.hokudai.ac.jp

https://doi.org/10.1142/S0129167X20501104Cited by:1 (Source: Crossref)

Abstract

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 $A$ -hypergeometric system is a theme of the book by Saito, Sturmfels and Takayama. Whereas they perturbed a parameter vector to obtain logarithmic $A$ -hypergeometric series solutions, we adopt a different perturbation in this paper.

Keywords:

AMSC: 33C70

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